Optics Question 959
Question: A glass slab has the left half of refractive index $ n _{1}, $ and the right half of $ n _{2}=3n _{1} $ . The effective refractive index of the whole slab is
Options:
A) $ \frac{n _{1}}{2} $
B) $ 2n $
C) $ \frac{3n _{1}}{2} $
D) $ \frac{2n _{1}}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Total time taken to travel distance d is:
$ \frac{d}{2n _{1}}+\frac{d}{2n _{2}}=d( \frac{n _{1}+n _{2}}{2n _{1}n _{2}} )=\frac{d}{n _{eff}}; $
$ n _{2}=3n _{1}\Rightarrow n _{eff}=\frac{3}{2}n _{1} $
$ =\frac{6\times 10^{5}cm}{1.0003-1} $
$ =0.2cm=2mm $
