Question

In a young double-slit apparatus the screen is rotated by 60° about an axis parallel to the slits. The slit separation is 3 mm, the slit-to-screen distance (at the central fringe) is 4 m, and the wavelength of light is 450 nm. The separation between the third dark fringe on either side of the central fringe is ______.

Options

• 6 mm

• 8 mm

• `4sqrt3` mm

• `2sqrt3` mm

Answer 1

In a young double-slit apparatus the screen is rotated by 60° about an axis parallel to the slits. The slit separation is 3 mm, the slit-to-screen distance (at the central fringe) is 4 m, and the wavelength of light is 450 nm. The separation between the third dark fringe on either side of the central fringe is 6 mm.

Explanation:

Given, d = 3 mm; D = 4 m

λ = 450 nm; θ = 60°

In YDSE, the n^th position of dark fringe is given by,

`y_n = ((2n - 1))/2 (lambdaD)/d`

For 3^rd dark fringe,

`y_3 = (5lambdaD)/(2d) = 5/2 xx (450 xx 10^-9 xx 4)/(3 xx 10^-3)` = 1.5 mm

From the diagram,

`y^' = y/costheta = y/(cos60^circ) = 2y`

∴ `y^' = 2 xx 1.5 = 3` mm

The total distance between the 3^rd dark fridge on both sides is,

d' = 2y' = 6 mm