Optics Question 950
Question: The refractive index of air is 1.0003. The thickness of air column which will have one more wavelength of yellow light $ (X=6000\overset{o}{\mathop{A}}) $ than in the same thickness in vacuum is
Options:
A) 2 mm
B) 2 cm
C) 2 m
D) 2 km
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let d in cm be the thickness of air column = thickness of vacuum column (given).
Number of waves of wavelength $ \lambda =6000\overset{o}{\mathop{A}}=6\times {{10}^{-5}}cm $ in a thickness d cm in vacuum is $ n _{v}=\frac{d}{\lambda } $
Since the refractive index of air $ \mu =1.0003, $ the wavelength in air will be $ {\lambda _{a}}=\frac{\lambda }{\mu } $
Therefore, number of waves of wavelength $ {\lambda _{a}} $ of air is $ n _{a}=\frac{d}{{\lambda _{a}}}=\frac{d\mu }{\lambda } $
Given that $ n _{a}+1=n _{v} $
Hence $ \frac{d\mu }{\lambda }+1=\frac{d}{\lambda } $
$ d=\frac{\lambda }{\mu -1} $
$ =\frac{6\times 10^{5}cm}{1.0003-1} $
$ =0.2cm=2mm $
