In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56, the central fringe shifts to the position of $7^{\text{th}}$ bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thickness of mica sheet is $\alpha \times 10^{-9} \mathrm{~m}$. The value of $\alpha$ is ______.

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Wave Optics

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56, the central fringe shifts to the position of

7^{th}

bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thickness of mica sheet is

α \times 1 0^{- 9} m

. The value of

α

is ______.

Answer: 5625

Solution

The mica sheet adds an optical path

(μ - 1) t

in one arm, shifting the pattern. For the central maximum to move to the position of the seventh bright fringe,

(μ - 1) t = 7 λ

. Hence

t = \frac{7 λ}{μ - 1} = \frac{7 \times 450}{0.56} = 5625 nm = 5625 \times 1 0^{- 9} m

. The value of

α

5625

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Integer answer

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