Question

The velocity of light in two different media are $2\times {10}^8{\text{ms}}^{-1}$ and $2.5\times {10}^8{\text{ms}}^{-1}$ respectively. The critical angle for these media is

• A. ${\sin }^{-1}\left(\frac{1}{4}\right)$
• B. ${\sin }^{-1}\left(\frac{1}{2}\right)$
• C. ${\sin }^{-1}\left(\frac{4}{5}\right)$
• D. ${\sin }^{-1}\left(\frac{1}{5}\right)$

Answer 1

The correct option is C ${\sin }^{-1}\left(\frac{4}{5}\right)$

$c_r-\text{speed of light in rarer medium}$

$c_d-\text{speed of light in denser medium.}$

As we know, the critical angle is,

$\sin C=\frac{1}{\mu }=\frac{1}{\left(\frac{c_r}{c_d}\right)}$

$\sin C=\frac{c_d}{c_r}=\frac{2\times {10}^8}{2.5\times {10}^8}=\frac{20}{25}$

$\sin C=\frac{4}{5}$

$C={\sin }^{-1}\left(\frac{4}{5}\right)$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.