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College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

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BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

Prove that, if I is the intensity of light transmitted by two polarizing filters with axes at an angle θ and I ' is the intensity when the axes are at an angle 90.0 ° θ , then I + I ' = I 0 , the original intensity. (Hint: Use the trigonometric identities cos ( 90.0 ° θ ) = sin θ and cos 2 θ + sin 2 θ = 1 .)

To determine

Prove that I+I'=Io

Explanation

Given info:

Intensity of transmitted light when angle is θ is I

Intensity of transmitted light when angle is 90θ is I'

Formula used:

The intensity of the transmitted wave is related to the incident wave by

  I=Iocos2θ

Here,

  I is the intensity of transmitted light

  Io is the intensity of incident wave

  θ is the angle between the direction of polarized light and the axis of polarizing filter

Calculation:

Let the intensity of incident light is Io.

The intensity of the wave transmitted from the polarizer at an angle θ is

  I=Iocos2θ...... (1)

The intensity of the wave transmitted from the polarizer at an angle 90θ is

  I'=Iocos290θ...... (2)

Adding Eq. (1) and Eq

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