Question

Light of wavelength $\lambda$ from a point source falls on a small circular obstacle of diameter d. Dark and bright circular rings around a central bright spot are formed on a screen beyond the obstacle. The distance between the screen and obstacle is D. then, the condition for the formation is right, is
(A) $\sqrt{\lambda }\approx {\displaystyle \frac{d}{4D}}$
(B) $\lambda \approx {\displaystyle \frac{d^2}{4D}}$
(C) $d\approx {\displaystyle \frac{{\lambda }^2}{D}}$
(D) $\lambda \approx {\displaystyle \frac{D}{4}}$

Answer 1

Hint :to solve this problem, we have to know about the light wavelengths and the relation between light wavelength and distance between screen and obstacles. We have to know about the interference of light which is a special phenomenon which shows the wave nature of light. For this interference of light we know that, two waves interfere with each other and crest and crest or trough and trough meet an amplitude of light becomes very large and then we say, there happens constructive interference.

Complete Step By Step Answer:
We know that rings are formed when constructive interference occurs between the light waves from two slits. So, we can say that the condition for this to happen is $\lambda \approx {\displaystyle \frac{d^2}{4D}}$
This is the right answer. So the right option will be option number b.

Note :
we have to know that there are two types of interferences, one is constructive interference and another one is destructive interference. We can get confused between these two interferences. When the amplitude of the waves increases because of the wave amplitudes reinforcing each other is known as constructive interference. And again we can say, when two waves are one eighty degrees out of phase then destructive interference occurs.