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Refraction through glass slab (lateral shift)

Reflection and refraction · Physics

Convex lens ray diagram

Interactive 3D

Move the object and watch parallel rays converge at the focal point while the image obeys 1/f = 1/v + 1/u.

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cm
3cm10cm

Study notes

A ray in air hits a glass slab (n = 1.50, thickness t = 6.0 cm) at 60° to the normal. Find (a) the refraction angle inside, (b) the lateral shift of the emergent ray, (c) the shift at near-normal incidence (θ₁ = 5°). Step 1: sinθ₂ = sin60°/1.5 = 0.8660/1.5 = 0.5773 → θ₂ ≈ 35.26°. Step 2: x = t·sin(θ₁ − θ₂)/cosθ₂ = 6.0 × sin(24.74°)/cos(35.26°) = 6.0 × 0.4182/0.8165 ≈ 3.07 cm. The emergent ray runs parallel to the incident ray but 3.1 cm sideways. Step 3: Small-angle: x ≈ t·θ₁(n−1)/n with θ₁ = 5° = 0.0873 rad: x ≈ 6.0 × 0.0873 × 0.5/1.5 ≈ 0.175 cm ≈ 1.75 mm — tiny, as expected; shift vanishes at normal incidence. Thicker slabs and steeper angles magnify the effect.

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