Q. In a two slits experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5 \times 10^{- 2}$m towards the slits, the change in fringe width is $3 \times 10^{- 5}$m. If separation between the slits is $10^{- 3}$m, the wavelength of light used is
A) $4500\ \mathring{\mathrm{A}}$
B) $3000\ \mathring{\mathrm{A}}$
C) $5000\ \mathring{\mathrm{A}}$
D) $6000\ \mathring{\mathrm{A}}$
Explanation
(d) $\beta = \frac{\lambda D}{d}$
$\beta^{'} = \frac{\lambda D^{'}}{d}$
$\beta - \beta^{'} = \frac{\lambda\left( D - D^{'} \right)}{d}$
$3 \times 10^{- 5} = \frac{\lambda \times 5 \times 10^{- 2}}{10^{- 3}}$
Or $\lambda = \frac{3 \times 10^{- 5}}{50} = 6 \times 10^{- 7}m = 6000\mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.