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Question

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


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Solution

Step 1: Given

Refractive index: μ=1.5

Apparent depth from one side: D1'=5cm

Apparent depth from another side: D2'=3cm

Step 2: Formula Used

D'=DμWhere D'is the apparent depth, D is the real depth and μ is the refractive index.

Step 3: Find the real depths

Calculate the real depth from the first side by using the formula.

D1'=D1μ5cm=D11.5D1=5cm×1.5D1=7.5cm

Calculate the real depth from another side by using the formula.

D2'=D2μ3cm=D21.5D2=3cm×1.5D2=4.5cm

Step 3: Find the thickness of the slab

Calculate the thickness of the slab by adding both the real depths.

Thickness=D1+D2=7.5cm+4.5cm=12cm

The thickness (in cm) of the slab is 12cm.


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