Optics Question 877
Question: In a Young’s double slit experiment, if the incident light consists of two wavelengths $ {\lambda _{1}} $ and $ {\lambda _{2}} $ , the slit separation is d, and the distance between the slit and the screen is D, the maxima due to the two wavelengths will coincide at a distance from the central maxima, given by:
Options:
A) $ \frac{{\lambda _{1}}{\lambda _{2}}}{2Dd} $
B) $ ({\lambda _{1}}-{\lambda _{2}}).\frac{2d}{D} $
C) LCM of $ {\lambda _{1}}.\frac{D}{d} $ and $ {\lambda _{2}}.\frac{D}{d} $
D) HCF of $ \frac{{\lambda _{1}}D}{d} $ and $ \frac{{\lambda _{2}}D}{d} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ y _{n}=\frac{nD{\lambda _{1}}}{d}=\frac{(n+1)D{\lambda _{2}}}{d} $
or $ n=( \frac{{\lambda _{2}}}{{\lambda _{2}}-{\lambda _{1}}} ) $
and $ y _{n}=( \frac{{\lambda _{1}}{\lambda _{2}}}{{\lambda _{2}}-{\lambda _{1}}} )( \frac{D}{d} ) $ .
