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Diffraction of Light

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1. What is diffraction? Explain diffraction due to single

slit.

Ans:

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Diffraction : Light travels in straight line direction.

When an opaque obstacle is placed in front of light

source, the shadow of obstacle is formed. It is

observed that, the light rays which incident on the

edges of the obstacle, these light rays cannot travel

in straight line. These light rays are deviates.

Encroachment of light in the geometric shadow of

obstacle, takes place. This phenomenon is called

as diffraction of light.

i. observed by Garibaldi in 1665.

ii. studies by Newton and Hooks.

iii. Thomas Young was the first scientist who

applied a wave theory to this phenomenon. 3

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“The phenomenon of bending of light around

the corners of opaque obstacle and

encroachment of light in the geometries

shadow of opaque obstacle is called as

diffraction of light.”

ii. Diffraction of light is possible only when the size

of obstacle comparable to the wave length of

light.

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Diffraction due to single slit :

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2. Formation of first minima & first maxima on the

basis of Huygen’s wave theory.

According to Huygen’s theory, every point, on the

slit acts as secondary source of light. All the

secondary waves emitted, from all points O. These

all waves are in same phase, when reaches at

point O. Due to this maxima is formed at centre of

the screen as show in diagram.

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Formation of first minima :

i. According to Huygen’s wave theory, secondary

waves are travel in all possible direction. When

secondary waves makes an angle with the

direction of incident beam then few waves

reaches at point N, starting from point A and

point C. These waves are not in same phase.

There is a finite phase difference between

these waves starting from point A and C when

reaches at point NI as shown in the diagram. If

this phase difference is A/2 then point N, is a 7

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dark point, i.e. a dark band is formed.

Secondary waves are also emitting from point B

& C produces a dark point at N1.

ii. The path difference between the wave emitting

from B & C at point N1, is also

From the diagram, path difference between

point A & B is AD = AB sinθ = λ , because path

difference between AC is and between CB is

also AB sin θ = λ i.e. d sin θ = λ (AB = d)

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In the same way dark bands are produced at

points N2, N3, .............

iii. For first dark band we have the relation

d sin θ = λ .

For Second dark band dsin θ = 2 λ. Similarly

for nth dark band dsin λ = n θ. Values of θ is

different for different dark bands.

Formation of first maxima

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i. To explain the formation of first maxima (or first

secondary maxima), let us divide the slit in to

their equal sections as shown in diagram.

For specific angle, the secondary waves

emitting form two outer section cancels the

effect of each other i.e. wave emitting from

outer sections are in out of phase with each

other. The inner section produces a maxima at

M1 with less intensity.

ii. In the same way we can explain the formation

of second, third...... maxima by dividing the slit 10

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in to 5,7,9.... equal parts. From the diagram,

path difference for first maxima is AD = 3 λ / 2

i.e. path different between the end points of

each section is λ / 2 , There are three sections

therefore the path difference between point A

and B is 3 λ / 2 . From the diagram, path

different AD = d sin θ

d sin θ = 3 λ /2

This is the relation for first maxima.

For second maxima, path difference is

5 λ /2 d sin θ = 5 λ /2

For nth maxima, path difference is,

dsin θ = ( 2n + 1) λ / 2 where n = 1, 2, 3 .........

Rayleijh’s criteria for resolution of image.

i. “Separation of image of two objects, which

are very close to each other, using an

instrument is called as resolution of image.”11

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ii. When the image of point objects are formed

using optical instruments, these images are not

clear because of diffraction of light. Diffraction

pattern of two images which are separated by

limit distance is as show in diagram (a)

If the two objects are very close to each other,

diffraction pattern produced by two images is

overlapped and we cannot distinguish two

separate images as shown in diagram (b)

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iii. If such closed objects are seen through optical

instruments then these images are resolved.

The diffraction pattern after resolution is as

show in diagram (c)

These two images are appears to be a single

object.

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In this diffraction pattern the central maxima

due to first object i-overlapped on the first

minima due to second object and vice versa.

Due i this there are two peaks with small dip in

the middle. In this case we can say that the

objects are just resolved.

This is the limiting separation. According to

Lord Ray light if is called as limit of resolution of

two images.

“Two point sources of equal intensity are said to

be just resolves by an optical instrument if the

central maxima of diffraction pattern of one falls

on the first minima of the diffraction pattern due

to other.” OR

“The smallest separation between the two point

object at which they appear just separated is

called as limit of resolution of optical instrument

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and the reciprocal of limit of resolution is called

as resolving power of instrument.”

4. Explain resolving power of microscope and

telescope.

Ans:

Microscope is an optical instrument used to

magnify the object which is close to the instrument.

Telescope is an optical instrument used to magnify

the objects which are far away from the installment.

Resolving power of microscope :

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i. “Resolving power of microscope is defined as it

is the reciprocal of least separation between

two close objects, so that they appears just

separate, when observed through microscope.”

iii. According to Abbe the least distance of

separation so that the object gets separated

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using microscope is given as, According to

definition of resolving power of microscope,

Resolving power =

From this relation it is clear that, to get

maximum resolution

1. Refractive index p-must be large.

2. To increase the valve of q, aperture of

objective should be large.

In the above relation the term 2μ sin θ is called

as numerical aperture microscope.

Resolving power of telescope

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i. “Resolving power of telescope is defined as the

reciprocal of smallest angular separation

between two distant object, so that they

appears

ii. According to Airy, the angular separation is

given by instrument but the resolving power of

instrument is depends up of diffraction

phenomenon.

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