JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Wave Optics

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A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]

(A)94.8 nm
(B)68.7 nm
(C)137.5 nm✓ Correct
(D)275 nm

Answer: (C)

Solution

For maximum transmission through the film, the light reflected back at the two interfaces must interfere destructively, which for a higher-index film on a lower-index substrate corresponds to

2 μ t = nλ, n = 1, 2, 3, \dots

Minimum thickness corresponds to n = 1:

t_{min} = \frac{λ}{2 μ} = \frac{550}{2 ( 2.0 )} = \frac{550}{4} = 137.5 nm

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Single correct option

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