Key Points

The angle of incidence is equal to the angle of reflection ($\angle i = \angle r$). The incident ray, the normal to the mirror at the point of incidence, and the reflected ray all lie in the same plane.

A concave mirror has a reflecting surface curved inwards and is a converging mirror. A convex mirror has a reflecting surface curved outwards and is a diverging mirror.

For spherical mirrors with small apertures, the radius of curvature ($R$) is twice the focal length ($f$). The relationship is given by the formula $R = 2f$.

The mirror formula relates the object distance ($u$), image distance ($v$), and focal length ($f$) for all spherical mirrors: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.

Magnification ($m$) is the ratio of the height of the image ($h'$) to the height of the object ($h$). It is also related to object and image distance: $m = \frac{h'}{h} = -\frac{v}{u}$.

A concave mirror forms real and inverted images, except when the object is placed between the pole (P) and the principal focus (F), where it forms a virtual, erect, and enlarged image.

A convex mirror always forms a virtual, erect, and diminished image, irrespective of the object's position. This provides a wider field of view.

Refraction is the phenomenon of light bending as it travels from one transparent medium to another. This occurs because the speed of light changes between media.

The ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is a constant, known as the refractive index. This is Snell's Law: $\frac{\sin i}{\sin r} = \text{constant} = n_{21}$.

The absolute refractive index ($n$) of a medium is the ratio of the speed of light in vacuum ($c$) to the speed of light in the medium ($v$). The formula is $n = \frac{c}{v}$.

A convex lens is thicker at the center and converges light rays (converging lens). A concave lens is thinner at the center and diverges light rays (diverging lens).

The lens formula gives the relationship between the object distance ($u$), image distance ($v$), and focal length ($f$) for spherical lenses: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.

Magnification ($m$) produced by a lens is given by the ratio of image height ($h'$) to object height ($h$), and also by the ratio of image distance to object distance: $m = \frac{h'}{h} = \frac{v}{u}$.

The power ($P$) of a lens is the reciprocal of its focal length ($f$) in meters. The SI unit of power is the dioptre (D). The formula is $P = \frac{1}{f (\text{in m})}$.

Object distance ($u$) is always negative. For concave mirrors and lenses, focal length ($f$) is negative. For convex mirrors and lenses, focal length ($f$) is positive.