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Wave Optics

Question

Light of wavelength 6000 A⁰ is reflected at nearly normal incidence from a soap film of refractive index 1.4. The least thickness of the film that will appear black is

200 A⁰

2000 A⁰

1000 A⁰

Infinity

Solution

2000 A⁰

for the minimum in reflected light

2μtcosr =nλ

$t = \frac{nλ}{2 μcosr} t_{\min} = \frac{λ}{2 μ} = \frac{6000 A^{0}}{2 \times 1.4} = 2142 A^{0} ≃ 2000 A^{0}$