## Write an equation for the intensity of light after it has passed through all three polarizers in terms of the intensity of unpolarized light

Question

Write an equation for the intensity of light after it has passed through all three polarizers in terms of the intensity of unpolarized light entering the first polarizer I0 and the angle of the second polarizer relative to the first, given that the first and third polarizers are crossed (90° between them). Use trigonometric identities to simplify and give the results in terms of a single trigonometric function of φ = 2θ.

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3 years 2021-09-04T09:32:43+00:00 1 Answers 121 views 0

Explanation:

Intensity of unpolarised light = I₀

intensity after passing through first polariser =  I₀ / 2

Angle between first and second polariser is  φ so

intensity after passing through second polariser

= (I₀ / 2) cos²φ

Now angle between second and third polariser

= 90 – φ

intensity after passing though third polariser

= (I₀ / 2) cos²φ cos²( 90 – φ)

= (I₀ / 2) cos²φ sin²φ

= (I₀ / 8) 4cos²φ sin²φ

= (I₀ / 8) sin²2φ