Question
Hard
Solving time: 5 mins
Q.158. A plane monochromatic wave of natural light with intensity Iofalls normally on an opaque screen with round hole corresponding to the first Fresnel zone for the observation point P. Find the intensity of light at the point P after the hole was covered with two identical Polaroids whose principal directions are mutually perpendicular and the boundary between them passes
(a) along the diameter of the hole;
(b) along the circumference of the circle limiting the first half of the Fresnel zone.
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Text solutionVerified
(a) Assume first that there is no polaroid and the amplitude due to the entire hole which extends over the first Fresnel zone is A1
Then, we know, as usual,
When the polaroid is introduced as shown above, each half transmits only the corresponding polarized light. If the full hole were covered by one polaroid the amplitude transmitted w ill be
Therefore the amplitude transmitted in the present case will be through either half.
Since these transmitted waves are polarized in mutually perpendicular planes, the total intensity will be
(b) We interpret the problem to mean that the two polaroid pieces are separated along the circumference o f the circle limiting the first half o f the Fresnel zone. (This however is inconsistent with the polaroids being identical in shape; however no other interpretation makes sense.) From (5 .103) and the previous problems we see that the amplitudes o f the waves transmitted through the two parts is
and
and the intensity is
Then, we know, as usual,
When the polaroid is introduced as shown above, each half transmits only the corresponding polarized light. If the full hole were covered by one polaroid the amplitude transmitted w ill be
Therefore the amplitude transmitted in the present case will be through either half.
Since these transmitted waves are polarized in mutually perpendicular planes, the total intensity will be
(b) We interpret the problem to mean that the two polaroid pieces are separated along the circumference o f the circle limiting the first half o f the Fresnel zone. (This however is inconsistent with the polaroids being identical in shape; however no other interpretation makes sense.) From (5 .103) and the previous problems we see that the amplitudes o f the waves transmitted through the two parts is
and
and the intensity is
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Question Text | Q.158. A plane monochromatic wave of natural light with intensity Iofalls normally on an opaque screen with round hole corresponding to the first Fresnel zone for the observation point P. Find the intensity of light at the point P after the hole was covered with two identical Polaroids whose principal directions are mutually perpendicular and the boundary between them passes (a) along the diameter of the hole; (b) along the circumference of the circle limiting the first half of the Fresnel zone. |
Topic | Wave Optics |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 |
Upvotes | 76 |