Question

The refractive index of water is 4 / 3 and that of glass is 5/3. What will be the critical angle for the ray of light entering water from the glass?
A. ${\sin ^{ - 1}}(\dfrac{4}{5})$
B. ${\sin ^{ - 1}}(\dfrac{5}{4})$
C. ${\sin ^{ - 1}}(\dfrac{1}{2})$
D. ${\sin ^{ - 1}}(\dfrac{2}{1})$

Answer 1

The refractive index is nothing but the disturbance which is caused to wave while it is travelling. We can notice that the ray is incident on the glass and pass through the water. The direction of the ray is also important. The term critical angle is used in Snell’s law. We need to use Snell’s law formula to find the required answer.

Formula used:
${\mu _g}\sin {\theta _1} = {\mu _w}\sin {\theta _2}$
Where,${\mu _g}$= refractive index of glass
${\mu _w}$= refractive index of water
${\theta _1}$= incident angle or critical angle
${\theta _2}$= refracted angle

Complete step by step solution:

According to Snell’s law,
${\mu _g}\sin {\theta _1} = {\mu _w}\sin {\theta _2}$
Where,
${\mu _g}$= refractive index of glass
${\mu _w}$= refractive index of water
${\theta _1}$= incident angle or critical angle
${\theta _2}$= refracted angle
Now, we need to substitute the value of the refractive index of water and the refractive index of glass. The angle of refraction in water must be the right angle as we can see in the picture.
We get, ($\sin 90 = 1$)

$$\dfrac{5}{3}\sin \theta = \dfrac{4}{3}\sin 90 \\\ \sin \theta = \dfrac{{\dfrac{4}{3}}}{{\dfrac{5}{3}}} \\\ \theta = {\sin ^{ - 1}}\dfrac{4}{5} \\\$$

Hence, the correct option is (A).

Note: Snell’s law tells the relationship between incident angle and refracted angle along with the refractive index of both the medium. Angle between normal and ground will always be the right angle. Here is the tip that whenever you hear respectively then consider that each one value is assigned to different-different quantities but in a sequential manner. You can see this in the question explanation line. From the question you can see that the refractive index of glass is more than water. Hence we can say that it has high density and therefore it will cause more disturbances to wave.