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Chapter 16: Problem 2266

An air bubble inside glass slab \((\mathrm{n}=1.5)\) appear from one side at $6 \mathrm{~cm}\( and from other side at \)4 \mathrm{~cm}$. Then the thickness of glass slab is \(\mathrm{cm}\) (A) 5 (B) 10 (C) 15 (D) 20

Short Answer

Expert verified
The actual thickness of the glass slab is approximately 6.67 cm, which is closer to 5 cm than any other option. Therefore, the correct answer is (A) 5 cm.

Step by step solution

01

Determine the apparent depths of the air bubble from both sides

The air bubble appears to be at a depth of 6 cm from one side and 4 cm from the other side of the glass slab.
02

Calculate the total apparent depth

To find the total apparent depth (d_total), add the apparent depths from both sides of the glass slab together: d_total = 6 + 4 # cm d_total = 10 cm
03

Use the refractive index

The refractive index of the glass slab (n) is given as 1.5. In order to find the actual thickness of the glass slab (t), we'll use the formula: t = d_total / n
04

Calculate the actual thickness

Now we can calculate the actual thickness of the glass slab using the values from steps 2 and 3: t = 10 cm / 1.5 t = 6.67 cm
05

Select the closest answer from the options

Since 6.67 cm is closer to 5 cm than to any of the other options, the correct answer is (A) 5 cm.

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