Key ideas
Geometric optics follows light as rays. Rays bend when they cross a boundary between materials, and lenses and mirrors use that bending to form images.
- Snell’s law n₁ sin θ₁ = n₂ sin θ₂ relates the angles, which are measured from the normal. Light bends toward the normal when it enters a slower, higher-index medium.
- Total internal reflection happens when light tries to go from a higher to a lower index at an angle above the critical angle, sin θ_c = n₂ ÷ n₁.
- For a thin lens or mirror, 1 ÷ f = 1 ÷ dₒ + 1 ÷ dᵢ and the magnification is m = −dᵢ ÷ dₒ. A negative m means an inverted image.
- Speed of light in a medium is c ÷ n, and a lens of focal length f has power 1 ÷ f in diopters when f is in meters.
Key equations
n₁ sin θ₁ = n₂ sin θ₂sin θ_c = n₂ ÷ n₁1 ÷ f = 1 ÷ dₒ + 1 ÷ dᵢm = −dᵢ ÷ dₒP = 1 ÷ f (diopters)v = c ÷ n
Worked example
An object sits 30 cm from a converging lens of focal length 10 cm. 1 ÷ dᵢ = 1 ÷ 10 − 1 ÷ 30 = 2 ÷ 30, so dᵢ = 15 cm on the far side (a real image). The magnification is m = −15 ÷ 30 = −0.50, so the image is inverted and half the size of the object.
Common mistakes
- Measuring angles from the surface instead of from the normal.
- Using the wrong sign for virtual images. A virtual image has a negative image distance in the usual convention.
- Expecting total internal reflection when light goes from a lower to a higher index. It only happens the other way.
Practice
Test yourself with practice questions on this topic: Optics