ray optics

Second Year Physics study material 2015

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Ray Optics

(14 Marks weightage for Ray optics and Physical optics chapters)

1. Define Optics?

A) The branch of physics which describes about the phenomenon and laws associated

with generation and propagation of light and its interaction with matter is called

Optics.

Optics are broadly classified in to two categories

1. Geometrical optics ( if wavelength of light is smaller than size of obstacles)

2. Physical optics ( if wavelength of light is of the order of size of obstacles)

2. Define Reflection? State Laws of Reflection?

A) Reflection : The phenomenon of return of light in the same medium when the

light falls on a reflecting surface (say mirror) is known as reflection of light.

Reflection obeys certain laws known as Laws of Reflection

1. The angle of incidence is equal to angle of reflection.

2. The incident ray, reflected ray and normal to the reflecting surface at a point of

incidence all lie in the same plane.

Note :

3. Define Spherical mirror? How

many types of spherical mirrors

present?

A) Spherical mirror is a part of

spherical reflecting surface. They

are two types of spherical mirrors.

Concave mirror : It is a part of hollow

sphere having outer part (bulging

surface) silvered and the inner part

(depressed part ) as reflecting

surface . Concave mirror is also known as convergent mirror because it converges the

ray of light.


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Convex mirror : It is a part of hollow sphere having inner part (depressed surface)

silvered and the outer part ( bulging surface) as a reflecting surface. Convex mirror is

known as divergent mirror because it diverges ray of light.

4. Define Terminology associated with a spherical mirrors?

A) Center of curvature :

The center of sphere of which the spherical

mirror forms a part is called center of

curvature.

Radius of curvature :

The radius of a sphere of which the spherical

mirror form a part is called Radius of

curvature.

Pole : Mid point of spherical mirror is called

its pole

Principle axis : The line joining the center of curvature and the pole of spherical mirror

is called principle axis.

Aperture : It is the effective diameter of light reflecting area of mirror.

Principle focus : The point of the principle axis of a spherical mirror where the rays of

light parallel to the principle axis meet or appear to meet after reflection from the

mirror is called principle focus.

Focal length : The distance between the pole and the principle focus of spherical

mirror is called Focal length of a mirror.

5. Write a short note on sign conventions?

A) 1. All distances are measured from the pole of spherical mirror

2. Distances measured in the direction of light are taken as positive , while the

distances measured in the opposite direction of light is taken as negative.

3. The upward distances perpendicular to the principle axis are taken as positive,

while the distances measured downward to the principle axis are taken as negative.

6. Derive the relation between Radius of curvature and focal length of mirror?


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A) The distance between Pole and focal length of

mirror is called Focal length of mirror.

The distance between center of curvature and pole

of mirror is called Radius of curvature of mirror. To

find the relation between Focal length and radius of

curvature of mirror

Consider a Ray OA travelling parallel to principle

axis and incident on concave mirror at point A.

The light under goes reflection and passes through

the focal point of mirror. CA is the normal to the

mirror.

According to laws of reflection i = r =

Also ACF = OAC =

AFP is the external angle of ACF , so

AFP = ACF + CAF = + = 2

Now draw AN perpendicular to the principal axis

From right angled ANC , tan =

that is =

(if is small tan = ) -----(1)

From right angled ANF , tan 2 =

that is 2 =

(if tan2 = 2 ) ---------(2)

From 1 and 2 , we get 2

=

or NC = 2NF

As aperture of mirror is small, so point N lies very close to P .

NF = PF and NC = PC

Thus PC = 2PF -----(3) , using sign convection PC = -R and PF = -f ,

Hence equation (3) becomes R = 2f that is f =

7. Derive an expression for Mirror formula?

A) The relation between position of object (u) , position of mirror (v) and focal length (f) of

the mirror is known as mirror formula.

Distance between pole of mirror and position of

object on principle axis is represented by u. The

distance between pole of mirror and position of


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image on principle axis is represented by v and focal length of mirror is given by f.

Let AB be an object lying beyond the focus (F) of a concave mirror. A ray of light BL

which is parallel to the principle axis through the principal axis at F after reflecting

from the concave mirror and goes along LB . Another ray from B passes through the

center of curvature (c ) and strikes the mirror normally at point M. After reflection ,

this ray retraces its path and meets LB at B. so AB is the real image of the object AB.

Now triangle ABC and ABC are similar , therefore

AB/AB = CA/CA --------------------(1)

Now triangle ABP and ABP are similar , therefore

AB/AB = PA/ PA ------------------------(2)

From 1 and 2 , we get

CA/CA = PA/PA ---------------------(3)

As per New Cartesian sign convection all the distances are measured from the pole of

mirror , so

CA = (PC PA) and CA = (PA PC) ------------- (4)

Substituting the values of equations (4) in equations (3) we get,

(PC PC)/(PA PC) = PA/PA ---------------------- (5)

Applying New Cartesian sign convection , PA = -v , PC = -R , PA = -u

Hence equation (5) becomes , ( -R + v)/(-u+R) = -v/-u

uR uv = vu vR, we get , uR + vR = 2uV

dividing by uvR , we get 1/v + 1/u = 2/R

or 1/f = 1/u + 1/v

8) Define linear Magnification and express formula in convex and concave

mirrors?

A) Linear Magnification:

Linear Magnification produced by a mirror is defined as the ratio of the size of the

image to the size of the object. It is denoted by m.

If I =size of the image and


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O= size of the object

Then, magnification, m=I/O ----------------- (6)

Magnification produced by a concave mirror:

In the case of concave mirror, magnification may be positive or negative depending

upon the nature of the image of an object.

(a) When real image is formed

m=I/O=-v/u

(b) When Virtual image formed

m =I/O= v/-u

Magnification produced by a convex mirror:

m=I/O=-v/u

9) Define Refraction of light?

A) The phenomenon of change in direction of path of light when it goes from one medium

to another medium is called refraction of light.

This phenomenon occurs because of fact that speed of light changes when it goes from

one medium to another. When light goes from rarer medium to denser medium it

bends towards the normal. When light goes from denser medium to rarer medium it

bends away from the normal.

10) Write a short note on Refractive index of a material?

A) Absolute refractive index : It is defined as the ratio of speed of light in air/vacuum

to the speed of light in a medium.

n = c/v where c = speed of light in vacuum = 3 x 108 m/s

Relative refractive index : when light passes from one medium to other , the refractive

index of medium 2 relative to medium 1 is written 12 and is given by 12 = 1/2

=v1/v2

A medium having higher value of refractive index is called optically denser medium

while a medium having lower value of refractive index is called optically rarer medium.

11) what are Laws of Refraction ?

A) 1. Incident ray , Refracted ray, Normal to the interface at a point of incidence lie on

the same plane , they are all coplanar.


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2. The ratio of sine of angle of incidence to the sine of angle of refraction is constant

for any two given media. This is also known as snells law.

Sin i / sir r = constant

This constant is also known as relative refractive index of second medium with

respect to first medium

Sin i / sin r = n2/n1

n1sini = n2 sin r

11) Write a short note on Lateral shift of light ray when it passes through a glass

slab?

A) Consider a glass slab. Consider a ray AO

incident on slab at an angle of incidence i and

passing through a slab of thickness t. After two

refractions at the boundary, the ray emerge

parallel to the incident ray. The perpendicular

distance between the incident ray direction and

emergent ray direction is called lateral shift or

lateral displacement (x).

From figure , the distance PQ is called lateral

displacement or lateral shift.

From triangle PQO, sin (i-r) = PQ/OP

PQ = OP sin (i r)

x = OP sin (i r) ---------------- (1)

But cos r = OM/OP, OP = OM/cos r = t/ cos r ------------------- (2)

from (1) and (2)

x = t((sin (i-r))/cos r)

12) Write a short note on Apparent depth?

A) Let us consider a beaker filled with water up to certain

level. Let an object O lie at the bottom of beaker. The depth

AO is known as real depth. The ray of light OA is incident

normally on the surface of water, so it is undeviated and goes

along AB in to air.


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Another Ray of light OC , incident on the surface of water at an angle i and after

refraction bends away from the normal and travels along CD in to air.

The ray CD meets the refracted ray AB at point I when produced backwards. So I is

the image of object O. Thus the object appears at position I instead of O. The depth AI

is known as apparent depth of object O.

According to snells law wna = sin i/sin r -----------------(1)

From AOC , sin i = AC/OC and from AIC , sin r = AC/IC

substituting the values of sin i and sin r in equation (1) we get

wna = (AC/OC) x (IC/AC) = IC/OC

Since point C lies very close to A , so IC AI and OCAO

wna = AI/AO

since anw = 1/wna

anw = AO/AI = Real depth/Apparent depth

in general 1n2 = Real depth/Apparent depth

Normal shift in the object position is given by x = AO AI

= AO (1 AI/AO)

= AO (1-1/1n2)

In general x =t(1-1/n)

13. Define Total internal reflection?

A) The phenomenon of reflection of light that takes place , when a ray of light

travelling in a denser medium gets incident at the interface of the two media at an

angle greater than the critical angle for that pair of media.

Critical angle : The critical angle for a pair of media may be defined as the angle of

incidence in denser medium , for which angle of refraction in the rarer medium is 90

degree angle.

According to snell law the refractive index of rarer medium a with respect to denser

medium b is

bna = sin i / sin r

when the ray of light is incident at critical angle that is when i = C , r = 90 degrees


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then bna = sin C / sin 90

but bna = 1/anb

therefore anb = 1/sin C

Practically there will be no loss of light in total internal reflection.

14 . Explain briefly some applications of Total internal reflection?

A) Mirages : It is an optical illusion observed in deserts and coal tarred roads on a

hot day. The object such as a tree appears inverted and the observer gets impression

as if the inverted image has been formed by pool of water . This phenomenon is known

as mirage.

Due to intense heat, surface of earth becomes quite hot and temperature of air near

the surface of earth is maximum. Temperature of layers goes on decreasing when one

goes up. Therfore density as well as refractive index of air increases slightly for

higher layers.

Therefore a ray of light travelling from a point on a tree passes through air of

gradually decreasing refractive index and gets refracted more and more away from the

normal and accordingly angle of incidence goes on increasing. At a layer , when angle

of incidence is becomes greater than critical angle total internal reflection takes place.

Then ray of light starts traversing layers of increasing refractive indices and goes on

bending more and more towards the normal. ultimately when the ray reaches the eye

from the observer , it appears to be coming from the different point. Hence the

inverted image of the tree produces the impression of reflection from a pool of water.

Brilliance of diamonds:

Refractive index of diamond is 2.47 and the critical angle for diamond air interface is

23 degrees. Due to low value of critical angle , a diamond can be cut so as to have a

large number of faces. As such each ray of light on entering the diamond from a face

undergoes a series of total internal reflections from other faces , till the angle of

incidence inside the diamond greater than critical angle. As a result it shines very

brilliantly

Prisms :

A right angled isosceles prism is called Porro prism , can be used in periscope or

binocular. Refractive index of glass is 1.5 . Therefore critical angle is given by 41

degrees. When a ray of light falls on the face of right angled prism at angle greater

than 41 degrees, it will suffer total internal reflection. Right angled prism are used to

bend light through 90 and 180 degree respectively.


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Optical fibers :

Optical fibers are used to transmit light from one place to another place in a curved

path in a more effective manner. The optical fibers consists of thousands of strands of

a very fine quality glass or quartz of refractive index 1.7 or so. The thickness of strand

is 10-6 cm. The strands are coated with a layer of some material of refractive index

(about 1.5) .

When light is incident at a small angle at one end , it gets refracted into the strands

and gets incident on the interface of the fibers and the coating. Angle of incidence

being greater than the critical angle the ray of light undergoes total internal

reflections. It suffers total internal reflection again and again till the angle of

incidence greater than critical angle.

Optical fibers are used in variety of applications

1. They are used in the field of communication. They are used for transmitting and

receiving electrical signals which are converted into light.

2. The optical fibers can be used for medical investigations like endoscope etc.,

15. Explain briefly refraction at a spherical surface?

A) Spherical refracting surface is a refracting medium whose curved surface is a part

of sphere.

A point object O lies on the

principal axis at a distance u from

the pole of the convex refracting

surface in rather medium. A ray of

light from O incident the convex

surface at A. AC is the normal to

the convex surface. After refraction

at A, the ray enters the denser

medium and bends towards the

normal. The refracted way meets the principal axis at I which is the real image of the

object O. The distance of the image I from the pole of the convex surface is v.

Let , and be the angles made by the incident ray, refracted ray and the

normal respectively with the principal axis. Draw AN perpendicular on the principal

axis.


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From AOC, i=+ (i)

and from AIC, =r+ or =r- ..(ii)

, and are small angles (assumption),

Using the relation =l/r, we get =AN/NO, =AN/NC and =AN/NI ..(iii)

Then i= AN/NO + AN/NC AN/PO + AN/PC (iv)

and r= AN/NC - AN/NI AN/PC - AN/PI (v)

Since aperture of the spherical surface is assumed to be small, so point N lies very

close to point P.

NO PO, NC PC and NI PI

Now according to Snells law,

sin i/sin r =n2/n1 or n1sin i=n2sinr

Since angles i and r are also small, so

n1i=n2r (sin i=i and sin r=r) (vi)

Using eqns. (iv) and (v) in eqn. (vi), we get

n1[AN/PO + AN/PC] = n2[AN/PC - AN/PI]

or

n1/PO + n1/PC = n2/PC-n2/PI

or

n1/PO + n2/PC = n2 n1/PC . (vii)

Applying new Cartesian sign conventions,

PO=-u, PC=R, PI=v

Hence eqn. (vii) can be written as

- n1/u + n2/v = n2-n1/R

16. Write a short note on Lenses ?

A lens is a piece of transparent material bounded by two refracting surfaces out of

which at least one is curved.


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If thickness of a lens is small and its curved surface is spherical then the lens is

known as thin spherical lens. If the central portion of a lens is thinner than its edges it

behaves as a divergent lens known as concave lens.

similarly, if central portion of a lens is thicker than its edges then it behaves as a

convergent lens known as convex lens.

Uses : Lenses are commonly used to correct vision defects of human eye. They are also

used in microscopes, telescopes and cameras. They are used in cinematography and

in photography.

Choice of rays for ray diagram to locate the image of an object

Any two of the following may be selected for drawing ray diagrams.

(i) A ray of light starting from the top of the object and parallel to the principal axis of

lens passes through the second principal focus in the case of a convex lens or appear

to diverge from first principal focus in the case of concave lens.

(ii) A ray of light passes through first principal focus of a convex lens come sout

parallel to the principal axis on refraction or a ray of light appears to meet at principal

focus of a concave lens parallel to principal axis on refraction.

(iii) A ray of light passes undeviated on refraction through optical center of the lens.

17. Derive an expression for Lens Makers Formula ?

The formula giving relation between the focal length (f) of the lens, refractive index of

the material of the lens (n) and the radii of curvature of its surfaces (R1 & R2) is known

as Lens Makers Formula.

Assumptions made to derive Lens Makers Formula:


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(i) The lens is thin and all the distances are measured from the optical center of the

lens.

(ii) The aperture of the lens is small.

(iii) The object is a point object and lies on the principal axis.

(iv) The angle made by incident ray and refracted ray with the principal axis are small.

New Cartesian Sign Conventions:

(i) All the distances are measured from the optical center of the lens.

(ii) Distances measured in the direction of the propagation of incident light are taken

as positive while the distances measured in the direction opposite to the direction of

propagation of incident light are taken as negative.

Derivation for Convex lens.

Consider a lens made of a material of

absolute refractive index n2. This lens

is placed in a medium of absolute

refractive index n1(n1


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- n2/v1 + n1/v = (n1-n2)/R2

- n2/v1 + n1/v = -(n2-n1)/R2

- n1/u + n1/v = (n2-n1) (1/R1 1/R2)

or - 1/u +1/v = (n2/n1-1) (1/R1 1/R2)

But n2/n1 = n , Relative refractive index of lens with respect to rarer medium

- 1/u +1/v = (n-1) (1/R1 1/R2)

If the object is at infinity , image is formed at the principal focus of the lens that is u =

infinity , v = f

- 1/ +1/f = (n-1) (1/R1 1/R2)

1/f = (n-1) (1/R1 1/R2) , This equation represents Lens makers formula.

The same formula is suitable for concave lens . But in that case R1 is negative and R2

is positive , f is negative .

In thin lens approximation , the points P1 and P2 are very close to each other of lens .

By applying sign convention . P10 = -u and P2I = +v , we get

1/v - 1/u = 1/f

18) Write a short note on focal point of lens ?

A) Lens has two focal points

First principal focus : Position of an object on the principle axis of the lens for which

the image is formed at infinity , its is called principle focus. It is denoted by F1.

Second principle focus : The position of image on the principle axis of the lens whose

object lying at infinity is called second principle focus of the lens. It is denoted by F2.

19. Explain briefly choice of light rays for lens to form an image and alos define

Magnification formula of lens?

A) 1. Ray emitting from object parallel to principle axis of lens after refraction passes

through second principle focus or appears to diverge from first principle focus

2. A ray of light , Passing through optical center of lens , emerges with out any

deviation after refraction.

3. A ray of light passing through first principal focus ( for convex lens) or appearing to

meet at it ( for a concave lens) emerges parallel to principle axis after refraction.


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Linear magnification of lenses : It is defined as the ratio of the size of image to the size

of object. m = I/O = v/u

By applying sign convention, for erect ( and virtual) image formed by convex or

concave lens , m is positive while for an inverted image (and real) image , m is

negative.

20. Define power of lens?

A) Power of lens is defined as the reciprocal of focal length of lens and is expressed in

meters.

P = 1/f (in m) = 100/f (in cm)

Unit of power is dioptre.

Dioptre is defined as Power of lens is said to be one dioptre if its focal length is one

meter

21) Explain briefly theory regarding thin lenses in contact?

A) Consider two thin lens of focal lengths f1

and f2 respectively in contact with each

other. Let O be the point object placed on

the principle axis of lenses. If second lens is

not present, then the first lens forms an

image I1 of the object O at a distance v1 from

it.

-1/u + 1/v1 = 1/f1 ----------------- (1)

since second lens in contact with the first , so I1 acts as an object for the second lens

which forms the image I at a distance v from it

-1/v1 + 1/v = 1/f2 ---------------- (2)

Adding 1 and 2 we get , -1/u + 1/v = 1/f1 +1/f2 or 1/f1 +1/f2 = 1/F

(since -1/u + 1/v = 1/f)

Thus two lens in contact behave as single lens of focal length F. This single lens is

known as equivalent lens and its focal length F is called equivalent focal length.

If more than two lenses are in contact, then the equivalent focal length of combination

1/F = 1/f1+ 1/f2+1/f3+..


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Power of an equivalent lenses :

We know that power of lens is given by P = 1/f

If lens are in contact, then the equivalent power of lens is given by

P = P1 + P2+ P3 +..

consider the lens having magnifications m1, m2, m3 then the net magnification of

lens is given by m = m1 x m2 x m3 x..

These equivalent lens have many applications. we will use these things in Optical

instruments like telescope , microscope, camera etc.,

22) Define prism and derive an expression for Refraction through the prism?

A) A Prism is the portion of transparent refracting medium bounded by two plane

surfaces meeting each other along a straight edge.

The two plane surfaces are called refracting faces and the line along which these two

faces will meet is called refracting edge of prism. The angle between two refracting

faces is called angle of prism and is usually denoted by A.

Refraction through the prism :

ABC is the principal section of the prism of refracting angle A . Let a ray of light DE be

incident on the refracting surface AB of the prism at angle of incidence i. After

refraction at E the ray of light bends towards the normal NO and travels along EF.

The refracted ray again suffers a refraction at F and bends away from the normal NO

and travels along FG. The ray FG is called emergent ray. The ray made by the angle of

emergent ray with normal is called angle of emergence. when the emergent ray is

produced backwards it meets the incident ray produced forward at point O. The angle

between emergent ray and incident ray is called angle of deviation ().

Determination of angle of deviation :

The incident ray DE is deviated along EF at surface AB at the prism

HEF = HEO - FEO or 1 = i r1

1 is the deviation produced by the surface AB of the prism. similarly at surface AC ,

the ray EF is deviated along FG so

2 =e r2

where 2 is deviation produced by the AC surface of the prism


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Total angle of deviation = 1 + 2

or = i r1 + e r2 = (i +e) (r1 + r2)

From quadrilateral AEOFA

A +AEO + EOF + OFA = 360

But AEO = OFA = 90

A +90 + EOF + 90 = 360 or A + EOF = 180

From BOC , r1 + EOF + r2 = 180

r1 + EOF + r2 = A + EOF

therefore A = r1 +r2

Substituting this value in the equation = = = (i +e) (r1 + r2) = (i+e) A

Thus the sum of angle of deviation and the angle of prism is equal to the sum of

incident angle and angle of emergence.

Prism formula :

Angle of deviation depend on angle of incidence. The variation of angle of deviation

with angle of incidence for a triangular prism as shown in figure.

As the angle of incident of light increases , the angle of deviation decreases till it

becomes minimum. The position of prism at this minimum angle is called minimum

deviation position.

condition for minimum deviation as follows

when light ray incident on face AB of prism and refracted into prism we have

ang = sini/sinr1

when the refracted ray incident on the face AC of the prism and emerges out of the air

, we have gna = sinr2/sin e

since ang = 1/ gna = sin i/sinr1 = sin e/ sinr2

and i = e and r1 =r2

If the angles of base of prism are equal , then the refracted ray passes parallel to the

base of the prism when prism is in minimum deviation position.

The refractive index of material of prism in terms of angle of prism and angle of

minimum deviation is


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we know for prism + A = (i +e) and r1 + r2 = A

if = m , i =e and r1 =r2 =r

therefore by substituting these values in above equation + A = (i +e)

we get m + A = 2i or i = (A+ m)/2

also 2r = A or r = A/2

According to snell law n = sin i/sin r

Substituting the values of i and r we get n = sin ((A+ m)/2)/sin (A/2)

For small angle prisms m is very small and we get n = ((A+ m)/2)/(A/2)

it implies that thin prisms do not deviate much.

23) Write a short note on dispersion of prisms?

A) The phenomenon of splitting of light into its component colors is known as dispersion.The pattern of color components of light is called the spectrum of light. Dispersion takes place because the refractive index of medium for different wavelengths is different. The prism has probably split the incident white light into a band of colors. The various colors seen are Violet, Indigo, Blue, Green, Yellow, Orange and Red, The acronym VIBGYOR will help you to remember the sequence of colours. The band of the colored components of a light beam is called its spectrum.

The red light bends the least while the violet the most. Thus the rays of each color emerge along different paths and thus become distinct. It is the band of distinct colors that we see in a spectrum. Isaac Newton was the first to use a glass prism to obtain the spectrum of sunlight. He tried to split the colors of the spectrum of white light further by using another similar prism. However, he could not get any more colors. He then placed a second identical prism in an inverted position with respect to the first prism . allowed all the colours of the spectrum to pass through the second prism. He found a beam of white light emerging from the other side of the second prism. This observation gave Newton the idea that the sunlight is made up of seven colors. 24) How Rainbow is formed due to sunlight? A) Rainbow is formed due to dispersion of light suffering refraction and reflection in the droplets present in the atmosphere. Thus rainbow is combined effect of refraction , reflection and dispersion of light. Two types of rainbows are seen in the atmosphere 1. Primary rainbow


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2. Secondary rainbow Primary rainbow is formed due to two refractions at the surface and one reflection of light inside the droplets (tiny water drops) . Outer edge of primary rainbow is red and inner edge is violet.

Water droplet suspended in air acts as a glass prism. The red color deviated the least

and the violet color is deviated the most. Different colors of refracted sunlight falls on

the opposite side of the drop. The reflected color on reaching the lower surface of water

drop suffers refraction. The refracted colors are deviated further.

The violet color will be emitted when angle between beam of sunlight and light coming

out of the drop is 40 degrees. The red color will be emitted when beam of sunlight and

the light coming out of the drop is 42 degrees.

Secondary rainbow :

It is formed due to two refractions at the surface and two internal reflection inside the

droplet. Secondary rainbow is coloured band having violet colour on outside and red

colour on the inner side.

25. Write a short note on Scattering of light?

A) The blue colour of the sky, colour of water in deep sea, the reddening of the sun at sunrise and the sunset are some of the wonderful phenomena . The earths atmosphere is a heterogeneous mixture of minute particles. These particles include smoke, tiny water droplets, suspended particles of dust and molecules of air. When a beam of light strikes such fine particles, the path of the beam becomes visible. The light reaches us, after being reflected diffusely by these particles. The phenomenon of scattering of light by the colloidal particles gives rise to Tyndall effect The colour of the scattered light depends on the size of the scattering particles. Very fine particles scatter mainly blue light while particles of larger size scatter light of longer wavelengths. If the size of the scattering particles is large enough, then, the scattered light may even appear white.

Rayleigh scattering refers to the scattering of light off the molecules of the air and can

be extended to scattering from particles up to about a tenth of wavelength of light. It is

Rayleigh scattering off the molecules of air which gives us blue sky.

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The molecules of air and other fine particles in the atmosphere have size smaller than the wavelength of visible light. These are more effective in scattering light of shorter wavelengths at the blue end than light of longer wavelengths at the red end. The red light has a wavelength about 1.8 times greater than blue light. Thus, when sunlight passes through the atmosphere, the fine particles in air scatter the blue colour (shorter wavelengths) more strongly than red. The scattered blue light enters our eyes. If the earth had no atmosphere, there would not have been any scattering. Then, the sky would have looked dark Light from the Sun near the horizon passes through thicker layers of air and larger distancein the earths atmosphere before reaching our eyes However, light from the Sun overhead would travel relatively shorter distance. At noon, the Sun appears white as only a little of the blue and violet colours are scattered. Near the horizon, most of the blue light and shorter wavelengths are scattered away by the particles. Therefore, the light that reaches our eyes is of longer wavelengths. This gives rise to the reddish appearance of the Sun. Optical instruments : The devices which work on the principle of refraction, reflection or rectilinear propagation of light etc., are called Optical instruments. 26) Explain How Human Eye acts as optical instruments? What are defects

associated with an eye? what are its corrections?

A) Like a camera, a normal eye focuses light and produces a sharp image. The mechanisms by which the eye controls the amount of light admitted and adjusts to produce correctly focused images, however, are far more complex, intricate, and effective than those in even the most sophisticated camera.

Working :

Light entering the eye passes through a transparent structure called the cornea behind which are a clear liquid (the aqueous humor), a variable aperture (the pupil, which is an opening in the iris), and the crystalline lens. Most of the refraction occurs at the outer surface of the eye, where the cornea is covered with a film of tears. Relatively little refraction occurs in the crystalline lens because the aqueous humor in contact with the lens has an average index of refraction close to that of the lens. The iris, which is the colored portion of the eye, is a muscular diaphragm that controls pupil size. The iris regulates the amount of light entering the eye by dilating, or opening, the pupil in low-light conditions and contracting, or closing, the pupil in high-light conditions. The cornealens system focuses light onto the back surface of the eye, the retina, which consists of millions of sensitive receptors called rods and cones.


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When stimulated by light, these receptors send impulses via the optic nerve to the brain, where an image is perceived. By this process, a distinct image of an object is observed when the image falls on the retina.

Accomodation of eye : The eye focuses on an object by varying the shape of the pliable crystalline lens through a process called accommodation. The lens adjustments take place so swiftly that we are not even aware of the change. Accommodation is limited in that objects very close to the eye produce blurred images. The near point is the closest distance for which the lens can accommodate to focus light on the retina. This distance usually increases with age and has an average value of 25 cm. At age 10, the near point of the eye is typically approximately 18 cm. It increases to approximately 25 cm at age 20, to 50 cm at age 40, and to 500 cm or greater at age 60. The far point of the eye represents the greatest distance for which the lens of the relaxed eye can focus light on the retina. A person with normal vision can see very distant objects and therefore has a far point that can be approximated as infinity. Rods and cones vision: The retina is covered with two types of light-sensitive cells, called rods and cones. The rods are not sensitive to color but are more light sensitive than the cones. The rods are responsible for scotopic vision, or dark-adapted vision. The cones are concentrated in the fovea. These cells are sensitive to different

wavelengths of light. In day light conditions we can able to see various colours due to

this cone.

Defects in eye: The eye may gradually lose its power of accommodation. In such conditions, the person cannot see the objects distinctly and comfortably. The vision becomes blurred due to the refractive defects of the eye. There are mainly three common refractive defects of vision. These are

(i) myopia or near-sightedness, (ii) Hypermetropia or farsightedness,

Presbyopia. These defects can be corrected by the use of suitable spherical lenses. Myopia :


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Myopia is also known as near-sightedness. A person with myopia can see nearby objects clearly but cannot see distant objects distinctly. A person with this defect has the far point nearer than infinity. Such a person may see clearly upto a distance of a few metres. In a myopic eye, the image of a distant object is formed in front of the retina and not at the retina itself. This defect may arise due to (i) excessive curvature of the eye lens, or (ii) elongation of the eyeball. This defect can be corrected by using a concave lens of suitable power. A concave lens of suitable power will bring the image back on to the retina and thus the defect is corrected.

Hypermetropia : Hypermetropia is also known as far-sightedness. A person with hypermetropia can see distant objects clearly but cannot see nearby objects distinctly. The near point, for the person, is farther away from the normal near point (25 cm). Such a person has to keep a reading material much beyond 25 cm from the eye for comfortable reading. This is because the light rays from a closeby object are focussed at a point behind the retina. This defect arises either because

(i) the focal length of the eye lens is too long, or (ii) (ii) the eyeball has become too small.

This defect can be corrected by using a convex lens of appropriate power. Eye-glasses with converging lenses provide the additional focusing power required for forming the

image on the retina.

Presbyopia : The power of accommodation of the eye usually decreases with ageing. For most people, the near point gradually recedes away. They find it difficult to see nearby objects comfortably and distinctly without corrective eye-glasses. This defect is called Presbyopia. It arises due to the gradual weakening of the ciliary muscles and diminishing


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flexibility of the eye lens. Sometimes, a person may suffer from both myopia and hypermetropia. Such people often require bifocal lenses. A common type of bi-focal lenses consists of both concave and convex lenses. The upper portion consists of a concave lens. It facilitates distant vision. The lower part is a convex lens. It facilitates near vision. These days, it is possible to correct the refractive defects with contact lenses or through surgical interventions. 27) Explain briefly theory of Microscope? A) A Microscope is an optical instrument to see very small objects as magnified one. Principle : A simple microscope is based upon the fact that an object placed between the optical center and the focus of a convex lens forms a virtual , erect and magnified image on the same side of the lens. For distinct vision (eye focused on near point ) : Magnifying power of a simple microscope is defined as the ratio of angle subtended by the image at the eye to the angle subtended by the object at the eye when both are placed at the least distance of distinct vision independently. Let = Angle subtended by object at the eye when object is supposed to be kept at the least distance of distinct vision Let = Angle subtended by the image, when image is at the distance equal to the least distance of distinct vision. Magnifying power (M.P) = / since and are small angles , so using the relation = l/r, we get = AB/CA and = AP/CA = AB/CA (since AP =AB) Hence magnifying power is given by M.P. = (AB/CA ) / (AB/CA ) But M.P. = size of image /size of object But for convex lens = m = I/O = v/u since v = -D and u = -u (sign conventions) We get M.P. = -D/-u

M.P. = D/u ---------------(1)

For the lens , we have -1/u + 1/v = 1/f

Applying new Cartesian sign convention , u becomes u and v = -D , we get


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1/u 1/D = 1/f

1/u = 1/f + 1/D

Multiplying by D we get D/u = 1 + D/f --------------------- (2)

Substituting the value of 2 in 1 we get

Magnifying power = (1 + D/f)

For Normal vision ( Eye focused at infinity )

To see image with relaxed eye , image must be formed at infinity. The microscope is in

normal adjustment when the image is formed at infinity . that is v =

for perfectly relaxed normal eye , the far point is at infinity so that object must be

placed at the focus of lens

for the lens -1/u + 1/v = 1/f

Here u = -u and v = , therefore = 1/u = 1/f

Multiplying both sides by D , we get D/u = D/f

Magnifying power = / = (O/u)/(O/D) = D/u

But u =f , Magnifying power = D/f

Compound microscope :

A compound microscope consists of two suitable lenses to give large magnification by

compounding the magnification given by the lenses. This is used to see very small

objects.

Principle : When an object is placed infront of convex lens O at a distance between F0

and 2F0 , the real inverted and magnified image is formed on the other side of this

lens. If this image les within the focal length of another convex lens E of large aperture

then the image acts as an object for this lens. The final image produced by this lens is

virtual , inverted and highly magnified.

Theory : Let AB be an object which lies between F0 and 2F0 of lens L1. The real

inverted and magnified image AB is formed on the other side of this lens L1. The

position of the lens E or L2 is adjusted in such a way that the image of AB of AB is

formed on the same side at a least distance of distinct vision. The final image AB is

virtual , inverted and highly magnified as shown

Magnifying power :


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The magnifying power of a compound microscope is defined as the ratio of the angle

subtended by the final image at the eye to the angle subtended by the object at the eye

when both are at a distance of least distance of distinct vision.

Determination of Magnifying power :

we know that M.P. = /

since and are small angles , so using the relation = l/r , we get

= AB/C2A and = PA/C2A

Magnifying power / = AB/PA

Since PA = AB therefore M.P = AB/AB

Multiplying and dividing right hand side of above equation By AB we get

M.P = AB/AB X AB/AB = AB/AB X AB/AB

magnification for objective lens is given by m0 = AB/AB

and magnification for eye lens is given by me = AB/AB

so magnifying power can be written as M.P. = m0 X me

To determine m0 , m0 = AB/AB = v0/-uo

where vo , uo are the distance of object and image from the objective lens.

To determine me , me = AB/AB = v/ue

where v is distance of final image AB from eye piece

ue is distance of object AB from eye piece

Since final image is formed at a distance of distinct vision (near point D) so v = D

Hence me = D/ue

for an eye piece -1/u + 1/v = 1/fe

using sign convention , u = -ue , v = -D , we get

-1/-ue + 1/-D = 1/fe

1/ue 1/D = 1/fe


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Multiplying both sides with D , we get

D/ue -1 = D/fe

D/ue = 1 + D/fe

Hence me = 1 + D/fe

Magnifying power = v0/-u0 (1 + D/fe)

if final image if formed at infinity me = D/fe

Magnifying power = m0me

M.P. = v0/-u0 (D/fe)

In this case length of microscope L = v0 + ue

28) Explain briefly about Reflecting Telescope?

A) Telescope is an optical instrument to clearly observe the distant objects.

Telescopes are basically of two types a) Refracting type b) Reflecting type

Refracting type telescopes are again classified as Astronomical and Terrestrial

telescope

Reflecting type telescopes are of two types 1) Cassegrain type and 2) Newtonian type

The telescope is used to provide angular magnification of distant objects It also has an objective and an eyepiece. But here, the objective has a large focal length and a much larger aperture than the eyepiece. Light from a distant object enters the objective and a real image is formed in the tube at its second focal point. The eyepiece magnifies this image producing a final inverted image. The magnifying power m is the ratio of the angle subtended at the eye by the final image to the angle which the object subtends at the lens or the eye. Hence Terrestrial telescopes have, in addition, a pair of inverting lenses to make the final image erect. Refracting telescopes can be used both for terrestrial and astronomical observations. The main considerations with an astronomical telescope are its light gathering power and its resolution or resolving power. The former clearly depends on the area of the objective. With larger diameters, fainter objects can be observed. The resolving power, or the ability to observe two objects distinctly, which are in very nearly the same direction, also depends on the diameter of the objective.


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. The largest lens objective in use has a diameter of 40 inch (~1.02 m). It is at the Yerkes Observatory in Wisconsin, USA. Such big lenses tend to be very heavy and therefore, difficult to make and support by their edges. Further, it is rather difficult and expensive to make such large sized lenses which form images that are free from any kind of chromatic aberration and distortions. For these reasons, modern telescopes use a concave mirror rather than a lens for the objective. Telescopes with mirror objectives are called reflecting telescopes. They have several advantages. First, there is no chromatic aberration in a mirror. Second, if a parabolic reflecting surface is chosen, spherical aberration is also removed. Mechanical support is much less of a problem since a mirror weighs much less than a lens of equivalent optical quality, and can be supported over its entire back surface, not just over its rim. One obvious problem with a reflecting telescope is that the objective mirror focusses light inside the telescope tube. Another solution to the problem is to deflect the light being focussed by another mirror. One such arrangement using a convex secondary mirror to focus the incident light, which now passes through a hole in the objective primary mirror, is shown in Fig. 9.33. This is known as a Cassegrain telescope, after its inventor. It has the advantages of a large focal length in a short telescope. The largest telescope in India is in Kavalur, Tamil Nadu. It is a 2.34 m diameter reflecting telescope (Cassegrain). It was ground, polished, set up, and is being used by the Indian Institute of Astrophysics, Bangalore. The largest reflecting telescopes in the world are the pair of Keck telescopes in Hawaii,

USA, with a reflector of 10 metre in diameter

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