Question

a small air bubble in a glass slab appears to be 2.4 cm from the surface calculate the real depth of the bubble if the ri glass is 1.5​

Answer 1

Question:

A small air bubble in a glass slab appears to be 2.4 cm from the surface. Calculate the real depth of the bubble if the refractive index of glass is 1.5​?

Solution:

Apparent Depth, $D_{a}$ = 2.4 cm

Real Depth, $D_{r}$ = x cm               [Let it be x]

Refractive index of glass, $\mu_{g}$ = 1.5

$Refractive \ Index = \frac{Real \ Depth}{Apparent \ Depth}$

$\mu_{g} = \frac{D_{r}}{D_{a}}$

$1.5 = \frac{D_{r}}{2.4}$

$D_{r} = 1.5 * 2.4$

$D_{r} = 3.6 \ cm$

The real depth of the small air bubble in a glass slab from surface is 3.6 cm

Answer 2

Given:

A small air bubble in a glass slab has apparent depth of 2.4 cm from the surface . Refractive index of glass is 1.5

To find:

Real depth of the bubble.

Concept:

Light rays from the bubble undergo refraction at the glass - air interface as a result of which the light rays are deviated away from the normal.

If we extend the refracted ray backwards, the ray projects an image at a higher position as compared to the original object.

The higher position is the apparent depth , why the original position is the actual depth or real depth.

Calculation:

Let real or actual depth be "d" ;

Refractive Index of glass can be expressed in form of actual depth and apparent depth as follows :

$\therefore \: \mu = \dfrac{actual \: \: depth}{apparent \: \: depth}$

$= > 1.5 = \dfrac{d}{2.4}$

$= > d= 1.5 \times 2.4$

$= > d = 3.6 \: cm$

So real depth of bubble is 3.6 cm from surface.