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A postage stamp kept below a rectangular glass slab of refractive index 1.5 when viewed from vertically above it, appears to be raised by 7.0 mm. Calculate the thickness of the glass slab.

Refraction Plane Surfaces

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Answer

As we know,

Shift=Real depth×(11aμm)\text {Shift} = \text {Real depth} \times (1 – \dfrac{1}{m})

Given,

Shift in the image = 7 mm or 0.7 cm

Refractive index of the glass block = 1.5

So, substituting the values in the formula we get,

0.7=Real depth×(111.5)0.7=Real depth×0.51.5Real depth=0.7×1.50.5Real depth=2.10.7 = \text {Real depth} \times (1 – \dfrac{1}{1.5}) \\[0.5em] 0.7 = \text {Real depth} \times \dfrac{0.5}{1.5} \\[0.5em] \text {Real depth} = \dfrac{0.7 \times 1.5}{0.5} \\[0.5em] \Rightarrow \text {Real depth} = 2.1 \\[0.5em]

Hence, the thickness of glass slab = 2.1 cm.
(Thickness of glass slab is same as the real depth of the postage stamp).

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