A ray of light is incident at an angle of 45 o (relative to the normal) on a thin film of a liquid with an index of refraction of 2 . Assuming that the medium on both sides of the film is air, find th

Question

A ray of light is incident at an angle of $45^{o}$ (relative to the normal) on a thin film of a liquid with an index of refraction of $\sqrt{2}$ . Assuming that the medium on both sides of the film is air, find the minimum thickness of the film required for constructive interference in the reflected light for sodium light of wavelength $600 nm$ .

TestHub · Accepted Answer

From Snell's law 1 × sin 45 o = 2 sin r sin r = 1 2 r = 30 ° ∆ x = 2 μ t cos r For constructive interference in reflection 2 μ t cos r + λ 2 = n λ t min = λ 4 μ cos r t min = 600 nm 4 × 2 × cos30 o ≈ 122 nm

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