Q. Monochromatic light of wavelength $\lambda_{1}$travelling in medium of refractive index $n_{1}$enters a denser medium of refractive index $n_{2}$. The wavelength in the second medium is
A) $\lambda_{1}\left( \frac{n_{1}}{n_{2}} \right)$
B) $\lambda_{1}\left( \frac{n_{2}}{n_{1}} \right)$
C) $\lambda_{1}$
D) $\lambda_{1}\left( \frac{n_{2} - n_{1}}{n_{1}} \right)$
Explanation
(a) $n_{1} = \frac{c}{v_{1}} = \frac{v\lambda}{v\lambda_{1}} = \frac{\lambda}{\lambda_{1}}$
$n_{2} = \frac{c}{v_{2}} = \frac{v\lambda}{v\lambda_{2}} = \frac{\lambda}{\lambda_{2}}$
Now, $\ \frac{n_{1}}{n_{2}} = \frac{\lambda_{2}}{\lambda_{1}}$
Or ${\ \lambda}_{2} = \left( \frac{n_{1}}{n_{2}} \right)\lambda_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.