In young's double slit experiment performed using a monochromatic light of wavelength $\lambda$, when a glass plate $(\mu=1.5)$ of thickness $\mathrm{x} \lambda$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Wave Optics

In young's double slit experiment performed using a monochromatic light of wavelength

λ

, when a glass plate

(μ = 1.5)

of thickness

x λ

is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

(A)3
(B)2✓ Correct
(C)1.5
(D)0.5

Answer: (B)

Solution

When a glass plate of thickness

t

and refractive index

μ

is introduced in one path, the optical path difference introduced is:

Δ = (μ - 1) t

For the intensity at the central maximum position to remain unchanged (i.e., still be a maximum), this path difference must be an integer multiple of

λ

(μ - 1) t = nλ

Given

μ = 1.5

and

t = x λ

(1.5 - 1) \cdot x λ = nλ

0.5 x = n

x = 2 n

For

n = 1

, we get

x = 2

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Single correct option

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