PHYS222 - Waves and Optics

Any optical scenario (involving light) where the wavelength of light is negligible comapred to the size of the system, and where light may be assumed to travel in straight lines unless influenced by the system

An imaginary line perpendicular to the wave front. It shows the direction of propogation

The path taken by a light ray is such that its optical path length is stationary with respect to small changes in its path, i.e. the optical path length is approximately equal to that on other adjacent paths

A mirror-like reflection, meaning all incoming parallel rays are reflected as parallel rays

Whilst the law of reflection is obeyed locally, the microscopically rough surface of an object results in parallel rays being reflected in different direcitons

The angle of incidence is equal to the angle of reflection

For an incoming beam passing into a medium with a different refractive index;

$\mathit{n_a}\sin(\mathit{\theta_a})=\mathit{n_b}\sin(\mathit{\theta_b})$

$\mathit{\theta_C}=\arcsin(\mathit{n_2}/\mathit{n_1})$

Something from which light radiates. It may be emitting light itself, or it may be reflecting light from another source

An object with no physical extent in space

An object with physical extent (length/width/height)

A point in space which light rays appear to converge towards or diverge away from

A point towards which rays converge

A point from which rays appear to diverge, though no light actually passes through the point

The point C which is at the centre of the sphere of which the mirror or lens surface is part

The radius R of the sphere for which the mirror or lens surface is part

The point V at the centre of the optic surface

The line CV passing through the vertex and the centre of curvature

The distance between an object and the vertex of an optical interface

If the object is on the same side of the interface as the incoming light, then the object distance is positive. Otherwise, it is negative.

The distance between an image and the vertex of an optical interface

If the image is on the same side of the interface as the outgoing light, then the image distance is positive. Otherwise, it is negative.

When the centre of curvature is on the same side of the surface as the outgoing light, then R is positive. Otherwise, it is negative.

A mirror with a negative radius of curvature

A mirror with a positive radius of curvature

The distance from the vertex at which parallel rays converge. For a spherical mirror, it is half the radius of curvature: $\mathit{f=\frac{R}{2}}$

$\frac{1}{\mathit{d_0}}+\frac{1}{\mathit{d_i}}=\frac{1}{\mathit{f}}$

A ray parallel to the opitcal axis which passes through the focal point after reflection
A ray through the focal point which is reflected parallel to the optical axis
A ray through the centre of curvature, which is reflected back along its path
A ray to the vertex, which is reflected with the same angle as that which it was incident with, though in the opposite direction.

The ratio of the image height to the object height
$m=\mathit{\frac{h_i}{h_o}=-\frac{d_1}{d_o}}$

$\mathit{\frac{n_a}{d_o}+\frac{n_b}{d_i}\approx \frac{n_b-n_a}{R}}$

$\mathit{m=-\frac{n_a d_i}{n_b d_o}}$

$\frac{1}{\mathit{u}}+\frac{1}{\mathit{v}}=\frac{1}{\mathit{f}}$ where u is the object distance and v is the image distance

A lens with an edge thinner than the centre point (f>0)

A lens with edges thicker than the centre (f<0)

As the paraxial approximation breaks down, parallel rays no longer get focused to the same point, resulting in a blurring of the image

The index of refraction for materials tends not to be constant as a function of wavelength, and so different coloured light is focused at different points.