Question

An air bubble in a glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is ______.

पर्याय

• 8 cm

• 10 cm

• 12 cm

• 16 cm

Answer 1

An air bubble in a glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is 12 cm.

Explanation:

Given: Refractive index of glass, μ = 1.5

Apparent depth from one side = 5 cm

Apparent depth from opposite side = 3 cm

Let the actual thickness of the slab be t. When viewed from the top, the apparent depth d₁ is related to the real depth by:

d₁ = `t/μ`

Similarly, from the bottom:

d₂ = `(t - x)/μ`

But in this case, the air bubble is fixed, and the apparent depths seen from both faces are:

`x/μ` = 5 and `(t - x)/μ` = 3

Multiplying both equations by μ:

x = 7.5 cm and t − x = 4.5 cm

Add both:

t = x + (t − x)

= 7.5 + 4.5

= 12 cm