Q. In a two slit 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 charge 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) $6000\ \mathring{\mathrm{A}}$
B) $5000\ \mathring{\mathrm{A}}$
C) $3000\ \mathring{\mathrm{A}}$
D) $4500\ \mathring{\mathrm{A}}$
Explanation
(a) $\ \ \ \ \ \ \ \beta = \frac{\lambda D}{d}$
$\Rightarrow \ \ \beta \propto D$
$\Rightarrow \ \frac{\beta_{1}}{\beta_{2}} = \frac{D_{1}}{D_{2}}$
$\Rightarrow \ \frac{\beta_{1} - \beta_{2}}{\beta_{2}} = \frac{D_{1} - D_{2}}{D_{2}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \frac{\mathrm{\Delta}\beta}{\mathrm{\Delta}D} = \frac{\beta_{2}}{D_{2}} = \frac{\lambda_{2}}{d_{2}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \lambda_{2} = \frac{3 \times 10^{- 5}}{5 \times 10^{- 2}} \times 10^{- 3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 6 \times 10^{- 7}m = 6000\mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.