Question

Two polaroids are placed in the path of an unpolarized beam of light of intensity such that no light is emitted through the second polaroid. If now a third polaroid whose polarization axis makes an angle ${30}^{\circ }$ with polarization axis of the first is placed between these two polaroids, then the intensity of light emerging through the last polaroid will be

• A. $\frac{I_0}{16}$
• B. $\frac{3I_0}{16}$
• C. $\frac{I_0}{8}$
• D. $\frac{3I_0}{32}$

Answer 1

The correct option is D $\frac{3I_0}{32}$


Intensity through $1^{st}$ polaroid, $I_1=\frac{I_0}{2}$
Intensity through $2^{nd}$ polaroid, $I_2=\left(\frac{I_0}{2}\right){\cos }^2{30}^{\circ }=\frac{3I_0}{8}$

Intensity through $3^{rd}$ polaroid, $I_3=\left(\frac{3I_0}{8}\right){\cos }^2{60}^{\circ }\Rightarrow I_3=\frac{3I_0}{32}$