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

In a Young's double slit experiment, an angular width of the fringe is

0.3 5^{\circ}

on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index

7/5

, is

\frac{1}{α}

. The value of

α

Answer: 4

Solution

When the entire system is immersed in a medium of refractive index

μ

, the wavelength in the medium becomes:

λ_{medium} = \frac{λ _{air}}{μ}

Since the angular width is proportional to wavelength:

θ_{medium} = \frac{θ _{air}}{μ}

Given

θ_{air} = 0.3 5^{\circ}

and

μ = 7/5

θ_{medium} = \frac{0.35 \times 5}{7} = \frac{1.75}{7} = 0.2 5^{\circ} = \frac{25}{100}^{\circ} = \frac{1}{4}^{\circ}

Therefore,

\frac{1}{α} = \frac{1}{4}

, giving

α = 4

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Integer answer

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