Geometric Optics

Geometric optics treats light as rays that travel in straight lines and obey simple reflection and refraction laws. The thin-lens equation and mirror equation allow us to locate images formed by optical elements.

Key Concepts

Law of reflection: θᵢ = θᵣ
Snell's law: n₁sinθ₁ = n₂sinθ₂
Thin lens equation: 1/f = 1/dₒ + 1/dᵢ
Magnification: m = -dᵢ/dₒ
Critical angle for total internal reflection: sinθ_c = n₂/n₁

Key Equations

Snell's law

n_1\sin\theta_1 = n_2\sin\theta_2

Thin lens equation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Magnification

m = -\frac{d_i}{d_o} = \frac{h_i}{h_o}

Critical angle

\sin\theta_c = \frac{n_2}{n_1}\quad (n_1 > n_2)

Worked Example

Example Problem

Problem

An object is placed 30 cm from a converging lens with f = 10 cm. Find the image distance and magnification.

Solution

1/dᵢ = 1/f - 1/dₒ = 1/10 - 1/30 = 2/30 → dᵢ = 15 cm. m = -dᵢ/dₒ = -15/30 = -0.5 (inverted, half-size).

Practice

Exercises

7 problems

1 of 7

An object 40 cm from a converging lens (f=15 cm). Find the image distance dᵢ in cm.

Your answer

2 of 7

For the same setup (dₒ=40 cm, f=15 cm), find the magnification m.

Your answer

3 of 7

Light travels from glass (n=1.5) to air (n=1.0). Find the critical angle for total internal reflection in degrees.

Unlock Exercise 3