Optics Question 1088

Question: 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

[KCET 1996]

Options:

A) 4 : 1

B) 1 : 1

C) 1 : 4

D) 2 : 1

Show Answer

Answer:

Correct Answer: A

Solution:

As $ \beta =\frac{D\lambda }{d}\Rightarrow \frac{{\beta _{1}}}{{\beta _{2}}}=( \frac{D _{1}}{D _{2}} )\ ( \frac{{\lambda _{1}}}{{\lambda _{2}}} )\ ( \frac{d _{2}}{d _{1}} ) $

$ \Rightarrow 1=( \frac{D _{1}}{D _{2}} )\times ( \frac{1}{2} )\times ( \frac{1}{2} )\Rightarrow \frac{D _{1}}{D _{2}}=\frac{4}{1} $



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