Q. In two separate set-ups of the Young’s double slit experiment, fringes of equal width are observed when lights of wavelengths in the ratio 1:2 are used. If the ratio of the slit separation in the two cases is 2 : 1, the ratio of the distances between the plane of the slits and the screen in the two set-ups is
A) 4 : 1
B) 1 : 1
C) 1 : 4
D) 2 : 1
Explanation
(a) As $\beta = \frac{D\lambda}{d} \Rightarrow \frac{\beta_{1}}{\beta_{2}} = \left( \frac{D_{1}}{D_{2}} \right)\left( \frac{\lambda_{1}}{\lambda_{2}} \right)\left( \frac{d_{2}}{d_{1}} \right)$
$\Rightarrow 1 = \left( \frac{D_{1}}{D_{2}} \right) \times \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right) \Rightarrow \frac{D_{1}}{D_{2}} = \frac{4}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.