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Q.
The wavelength of light in air and some other medium are respectively $\lambda_a $ and $\lambda_m..$ The refractive index of medium is:
Rajasthan PMTRajasthan PMT 2003
Solution:
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, $\mu=\frac{\lambda_{a}}{\lambda_{m}}$