SATHEE: Optics Question 466

Optics Question 466

Question: In the ideal double-slit experiment, when a glass plate (refractive index 1.5) of thickness $t$ is introduced in the path of one of the interfering beams (wavelength $λ$ ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is

Options:

A) $2 λ$

B) $2 λ / 3$

C) $λ / 3$

D) $λ$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Path difference due to slab should be integral multiple of $λ$ . Hence, $Δ x = n λ$ Or $(μ - 1) t = n λ,$

$n = 1, 2, \dots$ Or $t = \frac{n λ}{μ - 1}$ For minimum value of t, n=1.

$∴ t = \frac{n λ}{μ - 1} = \frac{λ}{1.5 - 1} = 2 λ$

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Optics Question 466

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