   Chapter 27, Problem 90PE

Chapter
Section
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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