Question

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 change in fringe width is $10^{-3} m$. Then the wavelength of light used is (given that distance between the slits is $0.03\, mm$ )

• A. $4500 \,\mathring{A}$
• B. $5000 \,\mathring{A}$
• C. $5500 \,\mathring{A}$
• D. $6000 \,\mathring{A}$

Answer 1

Answer: (D)

Fringe width $\beta=\frac{\lambda D}{d}$
$\therefore \Delta \beta=\frac{\lambda \Delta D }{ d }$
or, $\lambda=\frac{\Delta \beta d }{\Delta D }=\frac{10^{-3} \times 0.03 \times 10^{-3}}{5 \times 10^{-2}}=\frac{10^{-3} \times 3 \times 10^{-5}}{5 \times 10^{-2}}$ $=6 \times 10^{-7} m =6000 \,\mathring{A}$