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JEE Main 202310 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
10 April
Shift
Morning Shift
Subject
Physics
Chapter
Wave Optics

JEE Main 2023 · 10 April · Morning Shift · Physics · Wave Optics

Unpolarised light of intensity 32W m ^ - 2 passes through the...

Unpolarised light of intensity 32Wm−232W{m}^{- 2} passes through the combination of three polaroids such that the pass axis of the last polaroids is perpendicular to that of the pass axis of first polaroids. If intensity of emerging light is 3Wm−23W{m}^{- 2}, then the angle between pass axis of first two polaroids is _________°°.Unpolarised light of intensity 32W m ^ - 2 passes through the combination of three polaroids such that the pass axis of

Correct answer

0

Step-by-step solution

Unpolarised light of intensity 32W m ^ - 2 passes through the combination of three polaroids such that the pass axis of

The given data is

I0=32Wm−2{I}_{0} = 32W{m}^{- 2}

If=3Wm−2{I}_{f} = 3W{m}^{- 2}

Thus, by substituting the value, we get

If=(I02cos⁡2θ)×cos⁡2(90°−θ)...(i){I}_{f} = \left(\dfrac{{I}_{0}}{2}\cos^{2}\theta\right) \times \cos^{2}\left(90 ° - \theta\right) . . . ( i )

⇒3=16(cos⁡2θ⋅sin⁡2θ)⇒ 3 = 16\left(\cos^{2}\theta \cdot \sin^{2}\theta\right)

⇒cosθ⋅sinθ=34⇒sin⁡2θ=32⇒θ=30°⇒ cos\theta \cdot sin\theta = \dfrac{\sqrt{3}}{4} ⇒ \sin 2\theta = \dfrac{\sqrt{3}}{2} ⇒ \theta = 30 °

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