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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 ______.
Options
8 cm
10 cm
12 cm
16 cm
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Solution
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
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