Question

Question (1) :

i) what is the lateral displacement and on what factors does it depend?

ii) A postage stamp appears to be raised by 7.0 mm when placed under a rectangular glass block of refractive index 1.5. Find the thickness of the glass block.
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Answer 1

Lateral Displacement is the perpendicular distance between the emergent ray from a glass slab and the incident ray produced forward. It depends upon the thickness of the glass slab, the angle of incidence and angle of refraction and since these two angles are related by refractive index, we can equally say that the lateral displacement depends upon the refraction index.

Given

Refractive index (μ) = 1.5

Let real depth ( thickness ) of glass block be x mm

Then apparent depth will be (x - 7) mm,

Applying the formula, μ = Real depth ÷ Apparent depth

1.5 = x ÷ (x - 7)

1.5 (x - 7) = x

1.5x - 10.5 = x

1.5x - x = 10.5

0.5x = 10.5

x = 10.5 ÷ 0.5

x = 21 mm

The thickness of the glass block = 21 mm