Question

Two polaroid A and B placed in such a way that the pass-axis of polaroid are perpendicular to each other. Now, another polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarised light is \(I_0\) then intensity of transmitted light after passing through polaroid B will be

• A. \(\frac{I_0}{4}\)
• B. \(\frac{I_0}{2}\)
• C. \(\frac{I_0}{8}\)
• D. zero

Hint:

Use Malus law at each polaroid. The first polaroid halves unpolarised light.

Answer 1

The Correct Option is C

Step 1: After A
Unpolarised light of intensity \(I_0\) falls to \(\frac{I_0}{2}\) after the first polaroid.

Step 2: After C
C bisects the angle, so its axis is at \(45^{\circ}\) to A. \(I=\frac{I_0}{2}\cos^245^{\circ}=\frac{I_0}{4}\).

Step 3: After B
B is at \(45^{\circ}\) to C. \(I=\frac{I_0}{4}\cos^245^{\circ}=\frac{I_0}{8}\). Option (C).

Final Answer:
The transmitted intensity is \(\frac{I_0}{8}\), option (C). \[ \boxed{\text{(C) } \frac{I_0}{8}} \]