Summary

Reflection is governed by the equation ∠i = ∠r ′ and refraction by the Snell’s law, sini/sinr = n, where the incident ray, reflected ray, refracted ray and normal lie in the same plane. Angles of incidence, reflection and refraction are i, r ′ and r, respectively
The critical angle of incidence \(i_{c}\) for a ray incident from a denser to rarer medium, is that angle for which the angle of refraction is 90°. For i > \(i_{c}\) , total internal reflection occurs. Multiple internal reflections in diamond (\(i_{c}\) ≅ 24.4°), totally reflecting prisms and mirage, are some examples of total internal reflection. Optical fibres consist of glass fibres coated with a thin layer of material of lower refractive index. Light incident at an angle at one end comes out at the other, after multiple internal reflections, even if the fibre is bent
Cartesian sign convention: Distances measured in the same direction as the incident light are positive; those measured in the opposite direction are negative. All distances are measured from the pole/optic centre of the mirror/lens on the principal axis. The heights measured upwards above x-axis and normal to the principal axis of the mirror/ lens are taken as positive. The heights measured downwards are taken as negative.
Mirror equation: \[ \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \] where u and v are object and image distances, respectively and f is the focal length of the mirror. f is (approximately) half the radius of curvature R. f is negative for concave mirror; f is positive for a convex mirror.
For a prism of the angle A, of refractive index \(n_{2}\) placed in a medium of refractive index \(n_{1}\), \[ n_{21}=\frac{n_{2}}{n_{1}}=\frac{\sin \left[\left(A+D_{m}\right) / 2\right]}{\sin (A / 2)} \] where \(D_{m}\) is the angle of minimum deviation.
For refraction through a spherical interface (from medium 1 to 2 of refractive index \(n_{1}\) and \(n_{2}\) , respectively) \[ \frac{n_{2}}{v}-\frac{n_{1}}{u}=\frac{n_{2}-n_{1}}{R} \] Thin lens formula \[ \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \] Lens maker’s formula \[ \frac{1}{f}=\frac{\left(n_{2}-n_{1}\right)}{n_{1}}\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \] \(R_{1}\) and \(R_{2}\) are the radii of curvature of the lens surfaces. f is positive for a converging lens; f is negative for a diverging lens. The power of a lens P = 1/f. The SI unit for power of a lens is dioptre (D): 1 D = 1 \(m^{–1}\) If several thin lenses of focal length \(f_{1}\) , \(f_{2}\) , \(f_{3}\) ,.. are in contact, the effective focal length of their combination, is given by \[ \frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}+\frac{1}{f_{3}}+\ldots \] The total power of a combination of several lenses is \[ P=P_{1}+P_{2}+P_{3}+\ldots \]
Dispersion is the splitting of light into its constituent colour.
Magnifying power m of a simple microscope is given by m = 1 + (D/f), where D = 25 cm is the least distance of distinct vision and f is the focal length of the convex lens. If the image is at infinity, m = D/f. For a compound microscope, the magnifying power is given by m = \(m_{e}\) × \(m_{0}\) where \(m_{e}\) = 1 + (D/\(f_{e}\) ), is the magnification due to the eyepiece and m o is the magnification produced by the objective. Approximately, \[ m=\frac{L}{f_{o}} \times \frac{D}{f_{c}} \] where \(f_{o}\) and \(f_{e}\) are the focal lengths of the objective and eyepiece, respectively, and L is the distance between their focal points.
Magnifying power m of a telescope is the ratio of the angle β subtended at the eye by the image to the angle α subtended at the eye by the object. \[ m=\frac{\beta}{\alpha}=\frac{f_{o}}{f_{e}} \] where \(f_{o}\) and \(f_{e}\) are the focal lengths of the objective and eyepiece, respectively,