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Physics / 08

Optics

Explore the behaviour of light through reflection, refraction, mirrors, lenses, optical instruments, and the wave nature of light.

What is light?

Light is electromagnetic radiation that can propagate through empty space. In many everyday situations, light can be modelled as travelling along straight rays.

Ray model Represents the direction in which light travels and is especially useful for analysing mirrors and lenses.
Wave model Describes phenomena such as interference, diffraction, and polarisation.

Reflection

Reflection occurs when light reaches a surface and returns into the original medium.

Law of reflection The angle of incidence equals the angle of reflection, with both measured from the normal to the surface.
Regular reflection Reflection from a smooth surface can produce a well-defined reflected image.
Diffuse reflection Rough surfaces scatter reflected light in many directions.

Mirrors

Curved mirrors can form images that differ in size, orientation, and position depending on where the object is located.

Mirror equation

1/f = 1/u + 1/v

f is focal length, u is object distance, and v is image distance. Sign conventions depend on the chosen convention.

Magnification

m = v/u

The sign and interpretation of magnification depend on the adopted optical sign convention.

Refraction

Refraction is the change in direction of light as it passes between media in which its speed is different.

The frequency of the light remains unchanged at the boundary, while its speed and wavelength can change.

Snell's law

n₁ sin θ₁ = n₂ sin θ₂

n₁ and n₂ are the refractive indices of the two media, while θ₁ and θ₂ are measured from the normal.

Refractive index

Refractive index describes how much the speed of light is reduced in a particular medium compared with vacuum.

Refractive index

n = c/v

c is the speed of light in vacuum and v is the speed of light in the medium.

Total internal reflection

When light travels from a more optically dense medium toward a less dense medium, sufficiently large angles of incidence can cause the light to be completely reflected back.

Critical angle The angle of incidence for which the refracted ray travels along the boundary.
Applications Optical fibres use repeated total internal reflection to guide light over long distances.

Lenses

Lenses use refraction to converge or diverge light. The two fundamental types are converging and diverging lenses.

Convex lens A converging lens that can bring parallel rays toward a focal point.
Concave lens A diverging lens that causes parallel rays to spread apart.
Thin lens equation

1/f = 1/u + 1/v

The exact signs depend on the optical sign convention being used.

Dispersion

Dispersion occurs because the refractive index of a material can depend on the wavelength of light.

White light can therefore separate into different colours when passing through suitable materials such as a prism.

Interference

When coherent light waves overlap, their amplitudes combine according to the principle of superposition.

Constructive interference Waves reinforce one another and produce greater intensity.
Destructive interference Waves partially or completely cancel, producing reduced intensity.

Diffraction

Diffraction is the spreading of waves when they pass through an opening or around an obstacle. It becomes particularly noticeable when the size of the opening is comparable to the wavelength.

Polarisation

Polarisation describes restricting the oscillations of a transverse wave to a particular direction.

The phenomenon provides important evidence that light has transverse wave behaviour.

Optical instruments

Lenses and mirrors can be combined to construct instruments that form enlarged or otherwise useful images.

Human eye The eye uses a variable-focus lens system to form an image on the retina.
Microscope Uses multiple lenses to produce a strongly magnified image of a small object.
Telescope Collects and magnifies light from distant objects, allowing astronomical observations.

Quick example

Apply the idea

Light travels through a material at 2.0 × 10⁸ m/s. Taking the speed of light in vacuum as 3.0 × 10⁸ m/s, find the refractive index.

Using:

n = c/v

n = (3.0 × 10⁸) / (2.0 × 10⁸)

Answer: The refractive index is approximately 1.5.