Question

The critical angle of a piece of object in air is 40°. Find the critical angle of same piece of
glass if it is immersed in water. (Horater =1.33)
(a299
(b) 40°
(c) 620
(d) 20°​

Answer 1

Given:

The critical angle of a piece of object in air is 40°.  (Horater =1.33)

To find:

Find the critical angle of same piece of glass if it is immersed in water.

Solution:

From given, we have,

The critical angle of a piece of object in air is 40°.

θg = 40°

The index of the refraction of the piece of the glass in air,

μg = 1 / sin θg

μg = 1 / sin 40°

∴ μg = 1.5

Now consider,

sin θw / sin r = μw / μg

sin θw / sin 90° = 1.33 / 1.5       (∵ given, μw = 1.33)

sin θw = 0.886

⇒ θw = sin^{-1} 0.886

∴ θw = 62°

Therefore, the critical angle of same piece of glass if it is immersed in water is 62°.

Answer 2

Given that,

Critical angle = 40°

Refractive index of water = 1.33

We need to calculate the refractive index of the piece of the glass in air.

Using formula of refractive index

$\mu=\dfrac{1}{\sin\theta_{c}}$

$\mu=\dfrac{1}{\sin40}$

$\mu=1.5$

We know that,

The critical angle is the angle of incidence at which the total internal reflection takes place.

$\sin i=\sin C$

We need to calculate the critical angle of same piece of  glass if it is immersed in water

Using formula of critical angle

$\dfrac{\sin i}{\sin r}=\dfrac{\mu_{water}}{\mu}$

$\dfrac{\sin C}{\sin r}=\dfrac{\mu_{water}}{\mu}$

Put the value into the formula

$\dfrac{\sin C}{\sin 90}=\dfrac{1.33}{1.5}$

$C=\sin^{-1}(\dfrac{1.33}{1.5})$

$C = 62^{\circ}$

Hence, The critical angle of same piece of  glass if it is immersed in water is 62°.

(c) is correct option.