Question

The wavelength of light in two liquids ${}^{\prime }{x}^{\prime }$ and ${}^{\prime }{y}^{\prime }$ is $3500\mathring{A}$ and $7000\mathring{A}$. Then the critical angle of $x$ relative to $y$ will be :

• A. ${60}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is C ${30}^{\circ }$

We know that $v=\frac{c}{\mu }$

$\Rightarrow \frac{v_1}{v_2}=\frac{{\mu }_2}{{\mu }_1};{\mu }_1{\mu }_2=$refraction index

but $v=v\lambda ;v=$frequency, $\lambda$=wavelength

$\Rightarrow \frac{v{\lambda }_1}{v{\lambda }_2}=\frac{{\mu }_2}{{\mu }_1}\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{{\mu }_2}{{\mu }_1}$

$\Rightarrow \frac{3500}{7000}=\frac{{\mu }_y}{{\mu }_x}\Rightarrow \frac{{\mu }_y}{{\mu }_x}=\frac{1}{z}$

we know that critical angle of medium x relative to y will be $\theta =si{n}^{-1}\frac{1}{{\mu }_x/{\mu }_y}$

$\Rightarrow \theta =si{n}^{-1}\frac{1}{2}={30}^o$