Optics Question 862
Question: A light of wavelength $ 6000\overset{o}{\mathop{A}} $ shines on two narrow slits separated by a distance 1.0 mm and illuminates a screen at a distance 1.5 m away. When one slit is covered by a thin glass plate of refractive index 1.8 and other slit by a thin glass plate of refractive index $ \mu $ , the central maxima shifts by 0.1 rad. Both plates have the same thickness of 0.5 mm. The value of refractive index $ \mu $ of the glass is
Options:
A) 1.4
B) l5
C) 1.6
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Change in path difference for any point on screen is $ |\mu -1.8|t. $
For central maxima, phase difference = 0. Hence, $ d\sin \theta -|\mu -1.8|t=0 $
$ \Rightarrow d\theta =|\mu -1.8|t $ [q is very small and is in radian]
$ \Rightarrow | \mu -. 1.8 | .=\frac{{{10}^{-3}}\times 0.1}{0.5\times {{10}^{-3}}}=0.2\Rightarrow \mu =2 $ or 1.6
