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In double slit experiment, a light of wavelength $λ = 600 n m$ is used. When a film of material $3.6 \times 10^{- 3} c m$ thick was placed over one of the slits, the fringe pattern
was displaced by a distance equal to $30$ times that between two adjacent fringes. What is the refractive index of the martial?

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$8.1$

$5.5$

$7.2$

$1.5$

answer is A.

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Detailed Solution

Wavelength $λ = 600 n m = 600 \times 10^{- 9} m$

Thickness $t = 3.6 \times 10^{- 3} c m$

Number of fringes $n = 30$

Refractive index $μ = \frac{n λ}{t} + 1$ $(∵ n = \frac{(μ - 1) t}{λ})$

= $\frac{30 \times 6 \times 10^{- 7}}{3.6 \times 10^{- 5}} + 1$

$= 0.5 + 1$

$∴ μ = 1.5$

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