Question:
Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle \(30^{\circ}\) with each other. What fraction of incident unpolarised light is transmitted?
\[ \left(\cos 30^{\circ}=\sqrt{3} / 2\right) \]
Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle \(30^{\circ}\) with each other. What fraction of incident unpolarised light is transmitted?
\[ \left(\cos 30^{\circ}=\sqrt{3} / 2\right) \]
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The first polaroid halves the unpolarised intensity, and the second applies Malus's law.
Updated On: Nov 13, 2026
- \(57.5\%\)
- \(17.5\%\)
- \(27.5\%\)
- \(37.5\%\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
A polaroid transmits half of unpolarised light.
Polarised light then follows Malus's law: \(I = I_1\cos^2\theta\).
Step 2: First Polaroid
\(I_1 = \dfrac{I_0}{2}\)
Step 3: Second Polaroid
\(I_2 = \dfrac{I_0}{2}\cos^2 30^{\circ} = \dfrac{I_0}{2}\times\dfrac{3}{4} = \dfrac{3I_0}{8}\)
Step 4: Calculation
Fraction transmitted \(= \dfrac{3}{8} = 0.375 = 37.5\%\)
Final Answer:
Thirty-seven and a half percent of the incident light is transmitted. \[ \boxed{\text{(D) }37.5\%} \]
A polaroid transmits half of unpolarised light.
Polarised light then follows Malus's law: \(I = I_1\cos^2\theta\).
Step 2: First Polaroid
\(I_1 = \dfrac{I_0}{2}\)
Step 3: Second Polaroid
\(I_2 = \dfrac{I_0}{2}\cos^2 30^{\circ} = \dfrac{I_0}{2}\times\dfrac{3}{4} = \dfrac{3I_0}{8}\)
Step 4: Calculation
Fraction transmitted \(= \dfrac{3}{8} = 0.375 = 37.5\%\)
Final Answer:
Thirty-seven and a half percent of the incident light is transmitted. \[ \boxed{\text{(D) }37.5\%} \]
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