Question

Four polaroids are placed at an angle \(\theta\) with the optic axis of the preceding one. If unpolarised light of intensity 'I' falls on the first polaroid, the intensity of light transmitted from the fourth polaroid is
\([\cos \theta =X]\)

• A. \(\frac{IX^{2}}{2}\)
• B. \(\frac{IX^{4}}{4}\)
• C. \(\frac{IX^{6}}{2}\)
• D. \(\frac{IX^{8}}{4}\)

Hint:

The first polaroid halves the unpolarised light; each of the next three polaroids multiplies the intensity by cos squared theta.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Unpolarised light loses half of its intensity at the first polaroid. After that, every polaroid follows Malus's law: \(I = I_0\cos^{2}\theta\).

Step 2: Calculation
After the first polaroid: \(I_1 = \dfrac{I}{2}\).
The 2nd, 3rd and 4th polaroids each multiply the intensity by \(\cos^{2}\theta = X^{2}\).
So \(I_4 = \dfrac{I}{2}\left(X^{2}\right)^{3}\).

Step 3: Compare the options
\(I_4 = \dfrac{IX^{6}}{2}\), which matches option (C).

Final Answer:
The intensity transmitted from the fourth polaroid is IX^6/2. \[ \boxed{\text{(C) }\dfrac{IX^{6}}{2}} \]