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Total internal reflection and critical angle

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.

Controls

Drag the sliders or type a value — the simulation updates live.

cm
3cm10cm

Study notes

(a) Find the critical angle for glass (n = 1.50) to air. (b) A ray inside the glass hits the boundary at 50° to the normal — what happens? At 30°? (c) Find the critical angle for diamond (n = 2.42) and comment. Step 1: sinC = 1/n = 1/1.50 = 0.6667 → C = arcsin(0.6667) ≈ 41.8°. Step 2: At 50° > 41.8°: total internal reflection — 100% of the light reflects back into the glass, no refracted ray. At 30° < 41.8°: ordinary refraction (plus partial reflection); the ray exits into air bent away from the normal: sinθ₂ = 1.5 sin30° = 0.75 → θ₂ ≈ 48.6°. Step 3: Diamond: sinC = 1/2.42 = 0.4132 → C ≈ 24.4°. Much smaller than glass's 41.8° — light inside a diamond is far more likely to exceed C and be trapped, bouncing until it exits through the top: the physics behind a diamond's fire.

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