The wavelength of a monochromatic light in glass of refractive index 1.5 is 400 nm. The frequency of this light is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(5.0\times10^{14}\ \mathrm{Hz}\)
The frequency is the speed divided by the wavelength, both taken in the same medium. In glass the speed is \( c/n \).
\( \begin{aligned} v &= \frac{c}{n} \\ &= \frac{3\times10^{8}}{1.5} \\ &= 2\times10^{8}\ \mathrm{m\,s^{-1}} \end{aligned} \)
\( \begin{aligned} \nu &= \frac{v}{\lambda} \\ &= \frac{2\times10^{8}}{400\times10^{-9}} \\ &= 5.0\times10^{14}\ \mathrm{Hz} \end{aligned} \)
Hence, the frequency is \( 5.0\times10^{14} \) Hz. It is the same in air, because refraction does not change the frequency.
NCERT (2026-27):
Refraction of a plane wave – “… Now, if c represents the speed of light in vacuum, then,”
\( \displaystyle n_1=\frac{c}{v_1} \)\( \qquad (10.4) \)
“… are known as the refractive indices of medium 1 and medium 2, respectively.”
Refraction of a plane wave – “The above equation implies that when a wave gets refracted into a denser medium (v1 > v2) the wavelength and the speed of propagation decrease but the frequency ν(= v/λ) remains the same.”