Question

When a light ray is refracted from one medium into another, the wavelength changes from $4500\mathring{A}$ to $3000\mathring{A}$. The critial angle for a ray from second medium to first medium is:

• A. ${\sin }^{-1}\frac{2}{3}$
• B. ${\cos }^{-1}\frac{2}{3}$
• C. ${\tan }^{-1}\frac{3}{2}$
• D. ${\tan }^{-1}\frac{2}{\sqrt{5}}$

Answer 1

The correct option is A ${\sin }^{-1}\frac{2}{3}$

${\lambda }_1=450nm$ , ${\lambda }_2=300nm$

Refractive Index, ${}_1{\mu }_2=\frac{v_1}{v_2}$

$=\frac{\nu {\lambda }_1}{\nu {\lambda }_2}$

$=\frac{450}{300}=\frac{3}{2}$

${}_2{\mu }_1=\frac{2}{3}$ , again we know

${\theta }_c\left(criticalangle\right)=si{n}^{-1}{(}_2{\mu }_1)$

${\theta }_c=si{n}^{-1}\left(\frac{2}{3}\right)$