Chapter A: Reflection and Spherical Mirrors
The law of reflection — angle of incidence equals angle of reflection — governs all mirror optics. A plane mirror creates a virtual, erect, laterally inverted image of the same size at the same distance behind the mirror. Spherical mirrors are classified as concave (converging, f < 0 in Cartesian convention) and convex (diverging, f > 0). The fundamental relation f = R/2 connects focal length to radius of curvature. All mirror calculations use the formula 1/v + 1/u = 1/f with u always negative. Magnification m = −v/u: the negative sign is mandatory and is the primary source of NEET errors when students switch to lens problems.
Concave mirrors produce real inverted images for objects beyond F, and virtual erect magnified images for objects between F and P. Convex mirrors always produce virtual, erect, diminished images between P and F behind the mirror, making them suitable as rear-view mirrors.
Chapter B: Refraction, Snell's Law, and TIR
Snell's law n_{1} sin θ_{1} = n_{2} sin θ_{2} governs refraction at any interface. The refractive index n = c/v is dimensionless and always ≥ 1. Light bends toward the normal when entering a denser medium and away when entering a rarer medium. Total internal reflection (TIR) is the complete reflection of light with no transmitted ray. It requires two simultaneous conditions: the light must travel from a denser to a rarer medium (n_{1} > n_{2}), and the angle of incidence must exceed the critical angle θ_c = arcsin(n_{2}/n_{1}). Diamond has n = 2.42 and θ_c ≈ 24.4°, giving it its brilliant sparkle through repeated TIR at internal facets. Optical fibres transmit light signals by TIR at the core-cladding interface.
Chapter C: Thin Lenses
The thin lens formula 1/v − 1/u = 1/f differs from the mirror formula by the sign between terms (minus, not plus). For lenses, u < 0 (real object), convex f > 0, concave f < 0, and magnification m = v/u (no minus). Power P = 1/f (in metres), unit dioptre (D). Lens combinations in contact: P = + . The lensmaker's equation 1/f = (n−1)(1/ − 1/) relates focal length to material and geometry. A convex lens in water has a focal length approximately 4 times larger than in air (n_glass = 1.5), because the refractive contrast is reduced.
Chapter D: Prisms and Dispersion
A prism always deviates light toward its base. The total deviation is δ = (i + e) − A. Minimum deviation occurs when i = e and the ray passes symmetrically through the prism. The exact formula for refractive index at minimum deviation: n = sin((A + δ_m)/2)/sin(A/2). The thin prism approximation δ = (n − 1)A is valid only for small angles (A < 10°). Dispersion — differential deviation of different wavelengths — is characterized by dispersive power ω = (n_v − n_r)/(n_y − 1), a material property independent of the prism geometry.
Chapter E: Optical Instruments
Simple magnifier: M = 1 + D/f (image at D = 25 cm). Compound microscope: objective has short focal length f_o; eyepiece has longer focal length f_e; M = −(L/f_o)(D/f_e) at image infinity, where L is tube length. Astronomical telescope in normal adjustment: M = −f_o/f_e (negative → inverted image), L = f_o + f_e. The critical difference: microscope objective has SHORT f; telescope objective has LONG f. Eye defects (myopia, hypermetropia) are corrected by concave and convex lenses respectively, using the lens formula with appropriate object and image distances.