Question

The wavelength of light in air and some other medium are respectively ${\lambda }_a$ and ${\lambda }_m..$ The refractive index of medium is:

• A. ${\lambda }_a/{\lambda }_m$
• B. ${\lambda }_m/{\lambda }_a$
• C. ${\lambda }_a\times {\lambda }_m$
• D. None of these

Answer 1

Answer: (A)

The wavelength of light in air is
${\lambda }_a=\frac{c}{v}$ ...(1)
where $c=$ velocity of light in vacuum
$v=$ frequency of light
The frequency of light never change when it goes to any other medium
So, wavelength of light in medium is
${\lambda }_m=\frac{c}{\mu v}$ ... (2)
$\mu =$ refractive index of the medium
Dividing eq. (1) by eq.(2), we get
$\frac{{\lambda }_a}{{\lambda }_m}=\mu$
Hence, $\mu =\frac{{\lambda }_a}{{\lambda }_m}$