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Q.
The refractive index of water and glycerine are $1.33$ and $1.47 $ respectively. What is the critical angle for a light ray going from the later to the former?
Bihar CECEBihar CECE 2007
Solution:
When ray passes from denser to rarer medium, angle of refraction is greater than angle of incidence.
When a ray of light passes from glycerine (denser, $\mu=1.47$ ) to water (rarer, $\mu=1.33$ ) the angle of refraction (r) is greater than angle of incidence (i), than from Snells law
$\frac{\sin i}{\sin r}=\frac{\mu_{2}}{\mu_{1}}<1$
When $r=90^{\circ}$, corresponding angle of incidence is known as critical angle i.e., $i=\theta_{c}$.
$\therefore \frac{\sin \theta_{c}}{\sin 90^{\circ}}=\frac{\mu_{2}}{\mu_{1}}$
$\Rightarrow \sin \theta_{c}=\frac{\mu_{2}}{\mu_{1}}$
$\Rightarrow \theta_{c}=\sin ^{-1}\left(\frac{\mu_{2}}{\mu_{1}}\right)$
$=\sin ^{-1}\left(\frac{1.33}{1.47}\right)$
$\theta_{c}=64^{\circ} 48$