First slide

Young's double slit Experiment

Question

In a Young's experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength of monochromatic light used would be

Moderate

A

$60 \times 10^{- 4} cm$
B

$10 \times 10^{- 4} cm$
C

$10 \times 10^{- 5} cm$
D

$6 \times 10^{- 5} cm$

Solution

Distance of n^th dark fringe from central fringe
$x_{n} = \frac{(2 n - 1) λD}{2 d}$
$∴ x_{2} = \frac{(2 \times 2 - 1) λD}{2 d} = \frac{3 λD}{2 d}$
$\Rightarrow 1 \times 10^{- 3} = \frac{3 \times λ \times 1}{2 \times 0 .9 \times 10^{- 3}} \Rightarrow λ = 6 \times 10^{- 5} cm$

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