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Wave Optics

Question
CBSEENPH12039002
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Find an expression for intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?

Solution

Let us consider three polaroids A, B and C where C is kept in between A and B.

Using Malu’s Law, the intensity of light emerging from the middle polaroid C is given by,
straight I subscript 1 space equals space straight I subscript straight o cos squared straight theta space semicolon space straight I subscript straight o is straight space the straight space intensity straight space of straight space light straight space falling straight space on straight space middle straight space polaroid.
Therefore, intensity  falls on the polaroid at the end (polaroid B) whose polarisation axis makes an angle of (90 degree space – space straight theta right parenthesis spacewith the polarisation axis of the angle of middle polaroid.

Therefore, Intensity of light emerging from Polaroid B is, 
straight I subscript 2 space equals space straight I subscript 1 cos squared space left parenthesis space 90 minus straight theta right parenthesis space space space equals space left parenthesis straight I subscript straight o cos squared straight theta right parenthesis space cos squared left parenthesis 90 space minus space straight theta right parenthesis space italic space italic space italic space equals space straight I subscript o cos to the power of italic 2 θsin to the power of italic 2 straight theta space space space space equals space fraction numerator 1 over denominator 4 space end fraction straight I subscript 0 space left parenthesis 2 space sinθcosθ right parenthesis squared space straight I subscript italic 2 space equals space I subscript o over italic 4 sin to the power of italic 2 space 2 straight theta  

That is, transmitted intensity will be maximum when sin 2 straight theta = 1 
2 straight theta space equals space 90 to the power of straight o rightwards double arrow space space space space space space straight theta space space equals space 45 to the power of straight o

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases:
 Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth. 

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

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