Refraction at a Plane Surface - 2008

copyright© 2008 Dept.Of Physics, MDF(I) PU Science College,Sagar 1

Refraction at a plane surface The phenomenon of deflection of light ray from the path due to a change in its speed when it travels from one medium to another; it is called refraction. Absolute refractive index (n) of a particular medium- It is the ratio of speed of light in vacuum (c) to the speed of light in the given medium (v).

Mathematically vc

n =

Relative refractive index (n) of a pair of media- It is the ratio of absolute refractive index of one medium to the other.

Mathematically relative refractive index of medium (1) wrt medium (2) is 1

221 n

nn = ; read as

refractive index of medium (2) with respect to medium (1). TIP- In case of refraction through glass slab absolute

refractive index distance imagedistanceobject

depthapparent depth real

==n

Laws of refraction-

1. The incident ray, the refracted ray and the normal drawn at point of incidence all lie in the same plane

2. For a particular pair of media and for a particular wavelength the ratio of sine of angle of incidence to the sine of angle of refraction is always a constant.

constantsinrsini

=

• This is also called Snell’s law. • The ratio of sine of the angle of incidence to the sine of angle of refractive is a constant and is

the relative refractive index of the pair of media.

i.e. 211

2

nn

sinrsini n==

TIP – 1.vc

n = 2. 1

221 n

n=n 3.

2

121 v

v=n 4.

2

121 λ

λ=n

Probable Questions - 1.State and explain laws of refraction.(2marks) 2.State and explain Snell’s law.(2marks) 3.State the principle o f reversibility.(Ans: A light ray traveled over a path obeying laws of refraction it can be retraced in opposite direction.1mark) TIP – Always 1))(( 1221 =nn Lateral Shift(LS)- During refraction through the optical medium the perpendicular distance between the emergent ray and the incident ray is called the lateral shift. Expression for lateral shift (LS)-

• Consider a glass slab ABCD of refractive index n2 and thickness ‘t’ as shown aside

• It is surrounded by another medium of refractive index n1, let the medium is air

• Let us assume a light ray PQ falls at Q with an angle of incidence ‘i’ • Since the glass is denser light refracts along QR instead along QC

Refraction at a Plane Surface - 2008

copyright© 2008 Dept.Of Physics, MDF(I) PU Science College,Sagar 2

• Let the angle of refraction is ‘r’

• Applying Snell’s law to the surface AB: 1 2

sinsin

in

r= and to the surface CD: 2 1

sinsin '

rn

i=

But 1 22 1

1n

n= ; there fore sin 1 sin '

sinsin sinsin '

i irr ri

= = or sini=sini’;

This proves that the ray PQ||RS

• Consider the triangle RQT; )sin( QRRT

)sin( riQRRTorri −==− ------ (1)

• Consider another triangle NQR; r

tr

NQQRor

QRNQ

rcoscos

cos === ----- (2)

• Using (2) in (1) and since RT=perpendicular distance between refracted ray and the original path, RT=LS;

)sin(cos

rir

tLS −= is the expression for lateral shift

Probable Questions - 4.Define lateral shift. Deduce an expression for lateral shift in a glass slab.(5marks) 5.When i=0 what is LS?(1marks) Normal Shift (NS)- During refraction, the apparent shift in the position of the object along the normal is called normal shift. Expression of normal shift (NS)-

Consider denser medium ABCD of refractive index n1 and depth ‘t’ surrounded by another medium of refractive index n2; assuming that (1) is denser and medium (2) is rarer like air According to the definition normal shift NS= apparent shift in the position along the normal; i.e NS=OI=OP-IP ---- (1)

From ∆OPR; ORPR

i =sin ------ (2)

From ∆IPR; IRPR

r =sin ------ (3)

Now divide (3) by (2); sinsin

i IRr OR

=

Let us assume P and R are very much closer; then IR≈IP and OR≈OP

There fore the above relation becomes sinsin

i IPr OP

= ------ (4)

Apply Snell’s law to the surface AB at R; ri

nn

nsinsin

1

221 == ;

∴ 1 2n = IPOP

implies IP=OP.1 2n

By definition normal shift N s= real depth – apparent depth =OP – IP

Implies Ns = OP - OP. 1 2n = OP ( 1- 1 2n ) implies 2

1

1S

nN t

n

= −

If n1 = n and n2 =1 (air) then 1 1SN t

n = −

is the expression for the normal shift

[ Note : Normal sift in case of two or more media in contact Ns = Ns1 + N s2 + ……

implies total normal shift Ns = 11

11t

n

−

+ 22

11t

n

−

+ 33

11t

n

−

+ · · · · · · · ]

Refraction at a Plane Surface - 2008

copyright© 2008 Dept.Of Physics, MDF(I) PU Science College,Sagar 3

Probable Questions - 6.Define normal shift and deduce an expression for normal shift.(5mark) 7.A swimmer inside water watches a pole. How does it appear to him? 1.Streched 2.Dwarf 3.Skew 4.As it is. Critical angle(C)- Suppose a light ray is traveling from denser to rarer medium then for a pair of media and for a given wavelength the critical angle is that angle of incidence for which the angle of refraction is 90o. Let n be the refractive index of the denser medium and assuming air be the rarer medium

the following relation can be written; 21 2

1

sinsin

sin90n C

n Cn

= = =

Other wise sinC = 2

1

nn

TIP: For air as rarer medium nair=n rarer=1; 1

sindenser

Cn

=

Total Internal Reflection- Suppose a light ray is traveling from denser to rarer medium and if angle of incidence is greater than critical angle then the light ray reflects back to the denser medium, this phenomenon is called total internal reflection. Conditions to get total internal reflection- 1.Light ray should move from denser medium to rarer medium 2.Angle of incidence should be greater than critical angle of the denser medium. Probable Questions - 7.Define critical angle.(1marks) 8.What is a total internal reflection? Mention two conditions to get total internal reflection.(3mark) Mirages on land – During hot day time ground gets the heat and will be radiated back to the atmosphere. The air layer just above the ground gets more heat than the air above quite above the ground. Consider the diagram shown aside, there is an object OA and a light ray AB is coming from its tip A as shown. When it is coming towards ground it feels that the air layer at the bottom having less density than the toper, thus a low refractive indices. When the light ray reaches B the angle of incidence if greater than the critical angle for air, thus the light ray get reflected along BC; it is called total internal reflection.

Suppose a person watches thus moving light ray it may appear to come from point A′. Hence an inverted image OA′ will appear at the same position O. This is called mirage.

Probable Questions - 9.How does a mirage form? Explain.(4marks) Optical Fiber- An optical fiber is a micro glass rod coated with material of lower refractive index than glass. Suppose a light ray enters into the glass rod so that the angle of incidence is greater than the critical angle for glass, i.e i>C as shown the light ray reflects back the glass rod, this is called total internal reflection. Further the reflected ray gets multiple total internal reflections and from the other end of the glass rod light ray comes out.

Refraction at a Plane Surface - 2008

copyright© 2008 Dept.Of Physics, MDF(I) PU Science College,Sagar 4

The cladding with a material of lower refractive index is essential to get total internal reflection and the optical fibers are made used in the following fields; 1.In the medical field – As a tool to do endoscopes, etc., 2.In the field of communication – As a tool to transmit optical signals, like OFC technology, etc., 3.in the field of optical image capturing and editing Probable Questions - 10.What are optical fibers? Explain.(4marks) 11.Mention the uses of optical fiber.(2marks) 12.On what principle optical fiber works?(1mark)