Light of frequency \(6\times10^{14}\ \mathrm{Hz}\) has a wavelength of 375 nm in a liquid. The time taken by this light to cross a 9 cm deep layer of the liquid is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(4.0\times10^{-10}\ \mathrm{s}\)
The relation \( v=\nu\lambda \) holds inside the liquid too, with the wavelength measured in the liquid. This gives the speed, and the time follows from the depth.
\( \begin{aligned} v &= \nu\lambda \\ &= 6\times10^{14}\times375\times10^{-9} \\ &= 2.25\times10^{8}\ \mathrm{m\,s^{-1}} \end{aligned} \)
\( \begin{aligned} t &= \frac{d}{v} \\ &= \frac{0.09}{2.25\times10^{8}} \\ &= 4.0\times10^{-10}\ \mathrm{s} \end{aligned} \)
Hence, the light takes \( 4.0\times10^{-10} \) s to cross the layer.
NCERT (2026-27):
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.”