Question

A light ray of wavelength $600\, nm$ is incident on young's double slit experiment. Distance between slits is $2\, mm$ and $5^{\text {th }}$ bright fringe is at a distance of $3\, mm$ from central maxima, find the distance between slits and screen:

• A. 20 m
• B. 2 m
• C. 3 m
• D. 6 m

Answer 1

Answer: (B)

Given, $\lambda = 600 nm = 600\times10^{-9} m$
$d = 2 mm = 2 \times 10^{-3} m$
n = 5 and $x_{n} = 3 mm =3 \times 10^{-3} m$
Position of n$^{th}$ bright fringe from central maxima is, $x_{n} = \frac{n\lambda D}{d}=n\beta;\,$n = 0, 1, 2, ....
$\Rightarrow \,3\times10^{-3}= \frac{5\times600\times10^{-9}\,D}{2\times10^{-3}}$
$\Rightarrow \,D = \frac{3\times10^{-3}\times2\times10^{-3}}{5\times600\times10^{-3}}=2\,m$