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Question

The refractive index of a glass plate is 32. Then, the correct thickness of glass plate that will permit the same number of wavelengths as that by an 18 cm long column of water (μ=43) will be

A
12 cm
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B
16 cm
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C
20 cm
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D
24 cm
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Solution

The correct option is B 16 cm
Let the wavelength of light be λw in water and the total number of wavelengths be n.
Then, nλw=18 ...............(1)
Similarly,
Let the wavelength of light be λg in glass plate and the total number of wavelengths be n (same as in water).
Then, nλg=t ...............(2)
From (1) and (2),
λwλg=18t ...............(3)
We know that, relative refractive index,
gμw=μgμw=λwλg
3/24/3=18t
[from (3)]
t=16 cm
Why this question?
Tips: Here, the thickness of the medium will be an integral multiple of the wavelength of light.

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