Question

Light of frequency $\nu$, wave length $\lambda$ travelling with a velocity $v$ enters into a glass slab of refractive index $\mu$ then frequency, wave length and velocity of the wave in glass slab respectively are :

• A. $\frac{\nu }{\mu }$, $\lambda$, $\frac{v}{\mu }$
• B. $\nu$, $\frac{\lambda }{\mu }$, $\frac{v}{\mu }$
• C. $\nu$, $\lambda$, $\frac{v}{\mu }$
• D. $\frac{\nu }{\mu }$, $\frac{\lambda }{\mu }$, $\nu$

Answer 1

The correct option is B $\nu$, $\frac{\lambda }{\mu }$, $\frac{v}{\mu }$

We will use 3 concepts in this question:
1. Frequency of light does not change when light passes from one medium to another. Hence, when light enters a glass slab, it's frequency remains the same.
${\nu }_1={\nu }_2$
2. Refractive Index of medium 2 wrt medium 1 = (velocity of light in medium 1) / (velocity of light in medium 2)
$\mu =\frac{v_1}{v_2}$
As we know $\nu =v\lambda ⟹v_1{\lambda }_1=v_2{\lambda }_2$ as ${\nu }_1={\nu }_2$
Hence,
$\frac{v_1}{{\lambda }_1}=\frac{v_2}{{\lambda }_2}$
Rearrange$\frac{{\lambda }_1}{{\lambda }_2}=\frac{v_1}{v_2}=\mu$
Hence, ${\lambda }_2=\frac{{\lambda }_1}{\mu }$
Now for velocity:
Use ${\lambda }_2$ in formula 2
$v_2=\frac{\mu }{{\lambda }_2}$