Diffraction Of Light

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Question
ICSEENIPH12029760

What are the dark lines seen in the solar spectrum called?

Solution

Fraunhoffer lines.

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Question
ICSEENIPH12029777

With the help of a labelled diagram, show that fringe separation β in Young’s double slit experiment is given by:

                               straight beta space equals space λD over straight d
where the terms have their usual meaning.

Solution

Let S be a narrow slit luminated by monochromatic light, S1 and S2 be two parallel narrow slits very close to each other.
The light waves S reach S1 and S2 in some phase. According to Higgens principle S1 and S2 etc as new light sources from which secondary wavelet originate. These wavelet originate. These wavelets form interference fringes on screen.

Let a bright fringes be formed at P

Path difference. = (S2P - S1P)

ΔS2P - S1P = S2P - AP = S2A
 
In space increment straight S subscript 1 space straight S subscript 2 space straight A space sin space straight theta space equals space fraction numerator straight S subscript 2 straight A over denominator straight S subscript 1 space straight S subscript 2 end fraction

In space increment PCO space tan space straight theta space equals space OP over CO

sin space straight theta space rightwards arrow space space tan space straight theta space space rightwards arrow space straight theta

fraction numerator straight S subscript 2 straight A over denominator straight S subscript 1 space straight S subscript 2 end fraction space equals space OP over CO
fraction numerator
straight S subscript 2 straight A over denominator straight d end fraction space equals space straight x over straight p

straight S subscript 2 straight A space equals space xd over straight p
Position space of space bright space fringes comma space xd over straight D space equals space mλ
Dark space fringes comma space space xd over straight D space equals space left parenthesis 2 straight m space minus 1 right parenthesis straight lambda over 2
straight x space equals space left parenthesis straight m minus 1 half right parenthesis Dλ over straight d

Fringe space width comma space straight x subscript straight m space equals space mDλ over straight d
straight x subscript straight m plus 1 end subscript space equals space left parenthesis straight m plus 1 right parenthesis Dλ over straight d

Fringe space width comma space straight beta space equals space Dλ over straight d 

Question
ICSEENIPH12029778

(i) What is the difference between polarised light unpolarised light based on the direction of electric vector E?

(ii) What will be the effect on the width of the central bright fringe in the diffraction pattern of a single slit if :

(1)    Monochromatic light of smaller wavelength is used.

(2)    Slit is made narrower.

Solution

(i)
In unpolarised light the vibration of the electric vector E  occur symmetrically in all possible directions in a plane perpendicular to direction of propagation of light in polarised light the vibration of electric vector E occur in a plane perpendicular to the direction of propagation of light and are confined to a single direction in the plane.

(ii)
1. Width will decrease

2. When slit is made narrower the central bright fringe becomes wider.

Question
ICSEENIPH12029805

How did Fresnel construct a biprism in order to study interference of light?

Solution

Biprism is made from a single glass plate by grinding and polishing so that it is a single prism with one of its angle 179° and the other two about 30’ each.