Question

A ray of light travels from air to glass. It is found that the angle of refraction is half the angle of incidence. Then the angle of refraction is given by

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

Answer 1

The correct option is A ${\cos }^{-1}\left(\frac{n}{2}\right)$

A ray of light travels from air to glass.

It is given, that $r=\frac{1}{2}i$.

Where, $i$ is the angle of incidence and $r$ is the angle of refraction.

Now, according to Snell's law,

If $n$ be the refractive index of the glass,

$n=\frac{sini}{sinr}$

Or, $n=\frac{sin2r}{sinr}$

Or, $n=\frac{2sinrcosr}{sinr}$

[As we know, $sin2\theta =2sin\theta cos\theta$]

Now, $n=2cosr$

Or, $cosr=\frac{n}{2}$

$\therefore r=co{s}^{-1}\left(\frac{n}{2}\right)$

Therefore, the correct answer is - (A) $r=co{s}^{-1}\left(\frac{n}{2}\right)$