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Wave Optics

Question

Two Polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light I0 is incident on P₁. A third polaroid P₃
is kept in between P₁ and P₂ such that its axis makes an angle 45^o with that of P₁. The intensity of transmitted light through P₂ is

I₀/2

I₀/3

I₀/8

I₀/4

Solution

I₀/8

straight I subscript 2 space equals space straight I subscript 0 over 2 space cos squared space 45 space equals space straight I subscript 0 over 2 space straight x space 1 half space equals space straight I subscript 0 over 4 straight I subscript 3 space equals space straight I subscript 0 over 4 space cos squared space 45 to the power of 0 straight I subscript 3 space equals space straight I subscript 0 over 8