Example 1 · level 1
An equiconvex glass lens has both radii of curvature 30 cm and refractive index 1.6. Find its focal length (in cm, correct to 2 decimal places).
Show solution
- 1/f = 0.6 × 2/30
- f = 30 ÷ 1.2 = 25 cm.
Answer: 25 cm
CLASS 11–12 PHYSICS · RAY OPTICS
Lens maker's formula and prism
Lens maker's formula: 1/f = (n − 1)(1/R₁ − 1/R₂). For an equiconvex lens (R₁ = R, R₂ = −R): f = R/[2(n − 1)]. Prism at minimum deviation: n = sin((A + δm)/2) / sin(A/2).
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Worked examples
Example 2 · level 2
A plano-convex lens (n = 1.5) has a curved surface of radius 30 cm. Find its focal length (in cm).
Show solution
- 1/f = 0.5 × 1/30
- f = 30 ÷ 0.5 = 60 cm.
Answer: 60 cm
Example 3 · level 3
A prism of angle 60° gives a minimum deviation of 38°. Find the refractive index of the prism material (correct to 2 decimal places).
Show solution
- n = sin 49° ÷ sin 30° = 0.7547 ÷ 0.5 = 1.51.
Answer: 1.51