Question

A monochromatic ray of light passes from air to glass. The wavelength of light in air is $\lambda$, the speed of light in air is $c$ and in glass is $v$. If the refractive index of glass is $1.5$. The wavelength of light in glass is

• A. $1.5\lambda$
• B. $1.5/\lambda$
• C. $\lambda$
• D. $\lambda /1.5$

Answer 1

Answer: (D)

$\lambda /1.5$

From Snell's Law: $n_1{v}_1=n_2{v}_2$ and refractive index of air is $1.0$
Hence, $c=1.5v$
Frequency of light remains unchanged when travelling through any medium and $f=\frac{v}{\lambda }$ where $\lambda$ is the wavelength
Thus, equating frequencies in air and glass: $\frac{v_1}{{\lambda }_1}=\frac{v_2}{{\lambda }_2}$
Here given $v_1=c$; calculated $v_2=c/1.5$; given ${\lambda }_1=\lambda$
Thus, $\frac{c}{\lambda }=\frac{\frac{c}{1.5}}{{\lambda }_2}$ i.e. $\frac{c}{\lambda }=\frac{c}{1.5{\lambda }_2}$
Therefore; ${\lambda }_2=\frac{\lambda }{1.5}$