Ray Optics and Optical Instruments - Quick Revision
Reflection by spherical mirrors
- Mirror equation: 1/v + 1/u = 1/f; f = R/2.
- Sign convention (Cartesian): distances along incident light positive; f is negative for concave, positive for convex mirrors.
- Magnification m = h'/h = -v/u; negative m = real inverted image, positive m = virtual erect image.
Refraction and total internal reflection
- Snell's law: n = sin i/sin r; also n = c/v (speed ratio).
- n21 = 1/n12; bottom of a tank appears raised (apparent depth = real depth / n).
- TIR occurs when light goes from denser to rarer medium at i > critical angle C, where sin C = 1/n. Used in totally reflecting prisms and optical fibres.
Spherical surfaces and lenses
- Single spherical surface: n2/v - n1/u = (n2 - n1)/R.
- Lensmaker: 1/f = (n - 1)(1/R1 - 1/R2).
- Thin lens formula: 1/v - 1/u = 1/f; m = v/u.
- Power P = 1/f (dioptre, f in metres); positive for convex, negative for concave.
- Lenses in contact: 1/f = 1/f1 + 1/f2, i.e. P = P1 + P2; total magnification m = m1 m2 ...
Prism
- r1 + r2 = A and d = i + e - A.
- At minimum deviation i = e, r1 = r2, and mu = sin((A + Dm)/2)/sin(A/2).
- Thin prism: Dm = (n - 1)A.
Optical instruments
- Simple microscope: m = 1 + D/f (near point), m = D/f (infinity).
- Compound microscope: m = (L/fo)(D/fe); small fo and fe give large magnification.
- Telescope: m = fo/fe; tube length = fo + fe; large objective aperture gives more light and better resolution.