A rectangular glass block of refractive index 1.5 has an air bubble trapped inside it as shown in the diagram. When seen from the surface AB, it appears to be 4 cm deep.

(a) Calculate the actual depth of the air bubble from the surface AB.

(b) For which colour of light, blue or yellow, the apparent depth will be greater?

(c) Turning the glass block upside down, DOES NOT change the apparent depth of the air bubble. State True or False.

(a) Given,

Refractive index of glass = 1.5

Apparent depth of air bubble = 4 cm

As,

$\text {Refractive index of glass} = \dfrac{\text {Real depth of air bubble}}{\text {Apparent depth of air bubble}} \\[1em] ⇒ \text {Real depth of air bubble} = \text {Refractive index of glass}\times \text {Apparent depth of air bubble} \\[1em] = 1.5 \times 4 = 6 \text { cm}$

So, actual depth of the air bubble from the surface AB is 6 cm.

(b) As,

$\text {Refractive index of glass} = \dfrac{\text {Real depth of air bubble}}{\text {Apparent depth of air bubble}} \\[1em] ⇒ \text {Real depth of air bubble} = \text {Refractive index of glass}\times \text {Apparent depth of air bubble} \\[1em]$

Now, apparent depth will increase, if refractive index decreases and as wavelength increases, refractive index decreases. As wavelength of yellow light is greater than wavelength of blue light so, refractive index for yellow light is smaller than refractive index of blue light.

Hence, for yellow light apparent depth will be greater.

(c) When the block is turned upside down, then the real depth of the bubble is 15 – 6 = 9 cm

And,

$\text {Apparent depth of air bubble} = \dfrac{\text {Real depth of air bubble}}{\text {Refractive index of glass}}=\dfrac{9}{1.5} =6 \text { cm}\\[1 em]$

So, the statement is false.