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} $
