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Question

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I8. The angle between polarizer A and C is:


A

45°

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B

60°

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C

0°

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D

30°

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Solution

The correct option is A

45°


Step 1: Given

The initial intensity of light: I

The intensity of light after A: I1=I2

The intensity of light after B: I2=I2

The intensity of light after B when C is also placed: I3=I8

image

Step 2: Formula Used

Malus Law Formula: I=I0cos2θ

Step 3: Find the angle between A and C

When light passes through a polariser its intensity becomes half. Here, when the light passes through A its intensity becomes half and again when it passes through B its intensity remains same as after passing through A. This implies that A and B are parallel to each other. Now, find an expression after light passes through C using Malus law.

IafterC=I1cos2θ=I2cos2θ

Calculate the value of angle using Malus law and substituting values

I3=IafterCcos2θI8=I2cos2θcos2θcos4θ=14cosθ=12θ=45°

Hence, the angle between polariser A and C is 45°.


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