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In Young's double slit experiment, an interference pattern is obtained on a screen by a light of wavelength $6000 A^{0}$ coming from the coherent sources $S_{1}$ and $S_{2}$ . At certain point p on the screen fifth dark fringe is formed. Then the path difference $S_{1} p - S_{2} p$ in micron is

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2.7

4.5

5.4

1.5

answer is D.

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Detailed Solution

Wavelength $λ = 6000 A^{0} = 6000 \times 10^{- 10} m$

Number of fringes $n = 5$

Path difference $Δ x = (2 n - 1) \frac{λ}{2}$

$= (2 \times 5 - 1) \frac{6 \times 10^{- 7}}{2}$

$= \frac{(10 - 1) 6 \times 10^{- 7}}{2}$

$= \frac{9 \times 6 \times 10^{- 7}}{2} = \frac{5.4}{2}$

$∴ S_{1} P - S_{2} P = 2.7 m i c r o n s$

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