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} $

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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} ) $ .



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