Question

Three polaroid sheets are co-axially placed such that pass axis of polaroids \(2\) and \(3\) make \(30^{\circ }\) and \(90^{\circ }\) with pass axis of sheet. If \(I_{0}\) is the intensity of unpolarised light entering first sheet, the intensity of the emergent light through \(3^{rd}\) sheet is

• A. zero
• B. \(\frac{3I_{0}}{32}\)
• C. \(\frac{3I_{0}}{8}\)
• D. \(\frac{3I_{0}}{16}\)

Hint:

Unpolarised light halves in the first sheet, then Malus's law applies to each next sheet using the angle between consecutive pass axes.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Unpolarised light loses half its intensity in the first polaroid. After that, Malus's law \(I=I_{in}\cos^2\theta\) applies, where \(\theta\) is the angle between consecutive pass axes.

Step 2: After sheet 1 and sheet 2
\(I_1=\frac{I_0}{2}\).
Sheet 2 is at \(30^{\circ}\) to sheet 1, so \(I_2=\frac{I_0}{2}\cos^2 30^{\circ}=\frac{I_0}{2}\times\frac{3}{4}=\frac{3I_0}{8}\).

Step 3: After sheet 3
Sheet 3 is at \(90^{\circ}\) to sheet 1, so it is at \(90^{\circ}-30^{\circ}=60^{\circ}\) to sheet 2.
\(I_3=\frac{3I_0}{8}\cos^2 60^{\circ}=\frac{3I_0}{8}\times\frac{1}{4}=\frac{3I_0}{32}\).

Step 4: Compare the options
The emergent intensity is \(\frac{3I_0}{32}\), option (B).

Final Answer:
The emergent intensity is 3I0/32. \[ \boxed{\text{(B) }\dfrac{3I_{0}}{32}} \]