A bubble in glass slab $ (\mu = 1.5) $ when viewed from one side appears at 5 cm and 2 cm from other side, then thickness of slab is

Question

A light ray is passing from air (refractive index $ \mu_1 = 1.0 $) into water (refractive index $ \mu_2 = 1.33 $). If the angle of incidence in air is 30°, what is the angle of refraction in water?

Answer 1

To solve this problem, we need to understand the concept of apparent depth and real depth as it applies to refraction through a medium. Here, the medium is a glass slab with a refractive index \mu = 1.5.

The apparent depth d_a is related to the real depth d_r by the formula:

d_a = \frac{d_r}{\mu}

Given two observations from opposite sides of the slab, we have:

From one side, the bubble appears at an apparent depth of 5 cm.
From the other side, the apparent depth is 2 cm.

Let the real thickness of the slab be T. By the refraction formula, these observations can be written as:

From the first side: d_{1a} = \frac{T}{\mu} = \frac{T}{1.5} = 5 \, \text{cm}
From the second side: The light travels through the remaining thickness of the slab: d_{2a} = \frac{T - d_{1a} \mu}{\mu} = \frac{T - 5 \times 1.5}{1.5} = 2 \, \text{cm}

Substitute the value from step 1 into step 2:

2 = \frac{T - 5 \times 1.5}{1.5}

Simplifying the equation gives:

2 \times 1.5 = T - 7.5

3 = T - 7.5

T = 3 + 7.5 = 10.5 \, \text{cm}

Therefore, the thickness of the glass slab is 10.5 cm, which matches the given correct answer option.

Answer 2