Answer to Question #93272 in Optics for gautam jain

Question

8. Newton’s rings formed by monochromatic light between a flat glass plate and a plano-convex lens are viewed normally. Calculate the order of the dark ring which will have double the diameter of that of 40th dark ring.

Answer 1

For the given configuration, the radius of the nth dark ring is given by:

$$r_n^2=nR\lambda$$

So, the diameter is given by:

$$d_n=\sqrt{4nR\lambda}$$

So, the diameter twice as the diameter of the 40th dark ring has:

$$n=n_{40}*(\frac{d}{d_{40}})^2=40*2^2=40*4=160$$

So, the 160th order dark ring has the diameter twice as big as diameter of the 40th dark ring