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Refractive index

A glass plate of refractive index 1.5 is coated with a thin la

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Solving time: 4 mins

A glass plate of refractive index 1.5 is coated with a thin layer of thickness $t$ and refractive index 1.8. Light of wavelength $λ$ travelling in air is incident normally on the layer. It is partly reflected at the upper and the lower surfaces of the layer and the two reflected rays interfere. Write the condition for their constructive interference. If $λ = 648 nm$ , obtain the least value of $t$ for which the rays interfere constructively.

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Exam:

JEE Advanced 2000

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Amelia Discussed

A glass plate of refractive index 1.5 is coated with a thin layer of thickness

t

and refractive index 1.8. Light of wavelength

λ

travelling in air is incident normally on the layer. It is partly reflected at the upper and the lower surfaces of the layer and the two reflected rays interfere. Write the condition for their constructive interference. If

λ = 648 nm

, obtain the least value of

t

for which the rays interfere constructively.

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9 mins ago

Text solutionVerified

Incident ray

A B

is partly reflected as ray 1 from the upper surface and partly reflected as ray 2 from the lower surface of the layer of thickness

t

and refractive index

μ_{1} = 1.8

as shown in figure. Path difference between the two rays would by
Solution Image

Δ x = 2 μ_{1} t = 2 (1.8) t = 3.6 t

Ray 1 is reflected from a denser medium, therefore, undergoes a phase change of

π

, whereas the ray 2 get reflected from a rarer medium, therefore, there is no chang in phase of ray 2.
Hence, phase difference between rays 1 and 2 would be

Δ ϕ = π

. Therefore, condition of constructive interference will be

Δ x = (n - \frac{1}{2}) λ where n = 1, 2, 3 \dots or 3.6 t = (n - \frac{1}{2}) λ

Least value of

t

is corresponding to

n = 1

t_{m i n} = \frac{λ}{2 \times 3.6} t_{m i n} = \frac{648}{7.2} nm t_{m i n} = 90 nm

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Question Text	A glass plate of refractive index 1.5 is coated with a thin layer of thickness $t$ and refractive index 1.8. Light of wavelength $λ$ travelling in air is incident normally on the layer. It is partly reflected at the upper and the lower surfaces of the layer and the two reflected rays interfere. Write the condition for their constructive interference. If $λ = 648 nm$ , obtain the least value of $t$ for which the rays interfere constructively.
Topic	Ray Optics and Optical Instruments
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	75

Text solutionVerified

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