Question

Two slits are 1.0 mm apart and placed at a distance of 1.0 m from a screen.Find the fringe -width when light of wavelength 500 nm is used. What would be the fringe-width if the separation between the slits is halved and the distance of the screen from the slits is doubled?

• A. 1 mm, 2 mm
• B. 5 mm, 4.0 mm
• C. 0.5 mm, 2.0 mm
• D. 10 mm, 2.0 mm

Answer 1

The correct option is C 0.5 mm, 2.0 mm

Given,

$d=1mm=1\times {10}^{-3}m$

$D=1m$

$\lambda =500\times {10}^{-9}m$

We know that fringe width$\beta =\frac{\lambda D}{d}$

Substitute all value in above equation

$\beta =\frac{500\times {10}^{-9}\times 1}{1\times {10}^{-3}}=0.5mm$

Now

if $d=1/2mm=0.5\times {10}^{-3}m$

$D=2m$

$\lambda =500\times {10}^{-9}m$

We know that fringe width$\beta =\frac{\lambda D}{d}$

Substitute all value in above equation

$\beta =\frac{500\times {10}^{-9}\times 2}{0.5\times {10}^{-3}}=2mm$

Correct option is C.