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 $



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