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Physics 2 Unit 5: Geometric optics

Light travels in straight rays that reflect and refract, and mirrors and lenses form images predicted by ray diagrams and the thin-lens equation.

Covers: Reflection and plane mirrors, curved mirrors, refraction and Snell's law, total internal reflection, dispersion, thin lenses, ray diagrams, optical instruments

Study guide

In geometric optics, light travels in straight lines called rays. The law of reflection says the angle of incidence equals the angle of reflection, measured from the normal. A plane mirror forms a virtual, upright image the same size as the object, as far behind the mirror as the object is in front. Concave (converging) mirrors and convex (diverging) mirrors have a focal length f equal to half the radius of curvature (f = R/2).

Refraction is the bending of light as it changes speed between media. The index of refraction is n = c/v, where c is the speed of light in a vacuum. Snell's law states n₁ sin θ₁ = n₂ sin θ₂: light bends toward the normal when entering a medium with a higher index and away from it when entering a lower index. Light's frequency stays the same when it refracts, but its speed and wavelength change. Total internal reflection occurs when light travels from a higher index to a lower index at an angle greater than the critical angle, where sin θc = n₂/n₁; it's used in fiber optics. Dispersion occurs because n depends on wavelength, so prisms separate white light into colors.

Converging (convex) lenses bend light toward a focal point, while diverging (concave) lenses spread it out. The thin lens and mirror equation is 1/f = 1/do + 1/di, and magnification is M = hi/ho = −di/do. Sign conventions: f is positive for converging lenses and mirrors and negative for diverging ones; a positive di means a real image, and a negative di means a virtual image; a negative M means the image is inverted. Real images can be projected on a screen; virtual images can't. Ray diagrams use principal rays to locate images: an object outside the focal point of a converging lens forms a real, inverted image, and an object inside the focal point forms a virtual, upright, magnified image. Cameras, magnifying glasses, eyeglasses and telescopes all use these principles.

For mirrors, the principal rays are: a ray parallel to the axis reflects through the focal point (or appears to come from it, for a convex mirror), a ray through the focal point reflects parallel to the axis, and a ray to the mirror's center reflects at an equal angle. A convex mirror always forms a virtual, upright, smaller image, which is why it's used as a car's side mirror. When an object sits exactly at the focal point of a converging lens or concave mirror, the outgoing rays are parallel and no image forms. In the equation 1/f = 1/do + 1/di, di becomes infinite.

A mirror forms a real image on the same side as the object, where the reflected light actually goes. A lens forms a real image on the opposite side from the object. In both cases a positive di means a real image and a negative di means a virtual one.

Key ideas

• Angle of incidence equals angle of reflection.
• Snell's law: n₁ sin θ₁ = n₂ sin θ₂.
• Total internal reflection needs light going to a lower index above the critical angle.
• 1/f = 1/do + 1/di for mirrors and thin lenses.
• Real images are inverted and projectable; virtual images are upright.

Formulas and rules

Common mistakes

• Thinking frequency changes during refraction; speed and wavelength change instead.
• Mixing up sign conventions for diverging lenses (negative f).

Words to know

Ray

A line showing the path of light.

Law of reflection

Angle of incidence equals angle of reflection.

Normal

A line perpendicular to a surface.

Plane mirror

A flat mirror that forms virtual, upright images.

Concave mirror

A converging mirror that curves inward.

Convex mirror

A diverging mirror that curves outward.

Focal length

The distance from a mirror or lens to its focal point.

Refraction

The bending of light as it changes speed.

Index of refraction

n = c/v, the ratio of light's speed in vacuum to speed in a medium.

Snell's law

n₁ sin θ₁ = n₂ sin θ₂.

Critical angle

The angle beyond which total internal reflection occurs.

Total internal reflection

Complete reflection of light inside a denser medium.

Dispersion

Separation of light into colors by wavelength.

Converging lens

A lens that bends light toward a focal point.

Diverging lens

A lens that spreads light apart.

Real image

An image formed where light actually converges.

Virtual image

An image formed where light only appears to come from.

Magnification

The ratio of image height to object height.

Sample practice questions

15 more questions like these, from level 1 to 5, are in the practice set.