Question

In a Young's experiment, two coherent sources are placed 0.60 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 ____________.

Options

• 60 x 10^-4 cm

• 4 x 10^-4 cm

• 4 x 10^-5 cm

• 6 x 10^-5 cm

Answer 1

In a Young's experiment, two coherent sources are placed 0.60 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 4 x 10^-5 cm.

Explanation:

Distance of n^th dark fringe from central fringe,

`"y"_"n" = ((2"n"-1)lambda"D")/(2"d")`

`therefore "y"_2 = ((2 xx 2 - 1)lambda"D")/(2"d")`

`= (3lambda"D")/(2"d")`

`therefore 1 xx 10^-3`

` = (3 xx lambda xx 1)/(2 xx 0.6 xx 10^-3)`

`Rightarrow lambda = 4 xx 10^-5  "cm"`