Search any question & find its solution
Question:
Answered & Verified by Expert
A beam of light is incident from air on the surface of a liquid. The angle of incidence is $\theta$ and the angle of refraction is $\alpha$. If the critical angle for liquid when surrounded by air is $\theta_c$ then $\sin \theta_c$ is
Options:
Solution:
1566 Upvotes
Verified Answer
The correct answer is:
$\frac{\sin \alpha}{\sin \theta}$
Refractive index of liquid with respect to air,
$n_{l a}=\frac{\sin i}{\sin r}$
Here, $i=\theta$ and $r=\alpha$
So, refractive index of liquid with respect to air,
$n_{l a}=\frac{\sin \theta}{\sin \alpha}$
Now, if $\theta_c=$ angle of critical incidence for liquid then,
refractive index of air with respect to liquid is
$n_{a l}=\frac{1}{n_{l a}}=\frac{\sin \theta_c}{\sin 90^{\circ}}$
$\Rightarrow \sin \theta_c=\frac{1}{n_{l a}}=\frac{\sin \alpha}{\sin \theta}$
$n_{l a}=\frac{\sin i}{\sin r}$
Here, $i=\theta$ and $r=\alpha$
So, refractive index of liquid with respect to air,
$n_{l a}=\frac{\sin \theta}{\sin \alpha}$
Now, if $\theta_c=$ angle of critical incidence for liquid then,
refractive index of air with respect to liquid is
$n_{a l}=\frac{1}{n_{l a}}=\frac{\sin \theta_c}{\sin 90^{\circ}}$
$\Rightarrow \sin \theta_c=\frac{1}{n_{l a}}=\frac{\sin \alpha}{\sin \theta}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.