Key Points

Reflection follows the law that the angle of incidence equals the angle of reflection ($\angle i = \angle r$). Refraction is governed by Snell's Law, which states $\frac{\sin i}{\sin r} = n_{21}$, where $n_{21}$ is the refractive index of the second medium with respect to the first.

For spherical mirrors, the relationship between object distance ($u$), image distance ($v$), and focal length ($f$) is given by the mirror equation: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$. The linear magnification is $m = \frac{h'}{h} = -\frac{v}{u}$.

All distances are measured from the pole (for mirrors) or optical center (for lenses). Distances measured in the direction of incident light are positive, while those measured opposite to it are negative. Heights above the principal axis are positive.

When light travels from a denser to a rarer medium, it is completely reflected back if the angle of incidence exceeds the critical angle ($i_c$). The critical angle is defined by $\sin i_c = \frac{n_2}{n_1}$, where $n_1 > n_2$.

For refraction from a medium of refractive index $n_1$ to another of $n_2$ at a spherical surface with radius $R$, the formula is $\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$.

This formula relates a lens's focal length ($f$) to the refractive index of its material ($n_{21}$) and the radii of curvature of its two surfaces ($R_1$ and $R_2$): $\frac{1}{f} = (n_{21} - 1)(\frac{1}{R_1} - \frac{1}{R_2})$.

For a thin lens, the object distance ($u$), image distance ($v$), and focal length ($f$) are related by $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$. The magnification produced by the lens is $m = \frac{v}{u}$.

The power of a lens ($P$) measures its ability to converge or diverge light and is the reciprocal of its focal length in meters, $P = \frac{1}{f (\text{in m})}$. Its SI unit is the dioptre (D).

For multiple thin lenses in contact, the equivalent focal length ($f$) is given by $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} + \dots$. The total power is the algebraic sum of individual powers, $P = P_1 + P_2 + \dots$.

The refractive index ($n_{21}$) of the material of a prism is given by the formula $n_{21} = \frac{\sin((A + D_m)/2)}{\sin(A/2)}$, where $A$ is the prism angle and $D_m$ is the angle of minimum deviation.

A simple microscope uses a convex lens to produce a magnified virtual image. Its magnifying power is $m = 1 + \frac{D}{f}$ when the image is at the near point ($D \approx 25 \text{ cm}$), and $m = \frac{D}{f}$ when the image is at infinity.

A compound microscope uses an objective lens and an eyepiece for high magnification. Its total magnifying power is $m = m_o \times m_e$, which is approximately $m = \frac{L}{f_o} \times \frac{D}{f_e}$ for the final image at infinity, where L is the tube length.

A telescope provides angular magnification of distant objects. For a refracting telescope in normal adjustment (image at infinity), the magnifying power is $m = \frac{f_o}{f_e}$, and the tube length is $f_o + f_e$.

Modern telescopes often use a concave mirror as the objective instead of a lens to avoid chromatic aberration and for easier manufacturing of large apertures. A common design is the Cassegrain telescope.

Optical fibres transmit light over long distances with minimal loss using the principle of total internal reflection. They consist of a high refractive index core surrounded by a lower refractive index cladding.