Light and geometric optics
Geometric optics tests reflection, refraction, total internal reflection, thin lenses and mirrors, image formation and simple optical instruments. The PAU rewards correct ray reasoning and consistent sign conventions more than memorised cases.
Core rules
- Reflection: angle of incidence equals angle of reflection, measured from the normal. A plane mirror forms a virtual image behind the mirror at the same distance.
- Snell: n₁ sinθ₁ = n₂ sinθ₂, with n = c/v. Light bends toward the normal when entering a denser medium.
- Total internal reflection occurs only from higher to lower n, beyond the critical angle sinθ_c = n₂/n₁.
- Thin lens: 1/f = 1/d_o + 1/d_i; magnification m = h_i/h_o = -d_i/d_o. For a converging lens f > 0; for a diverging lens f < 0 in the usual Cartesian convention.
- Real images are formed by actual ray convergence and can be projected; virtual images cannot. A converging lens gives a real inverted image when d_o > f.
- Optical instruments use lenses to produce angular magnification; the eye and camera form real images, while a simple magnifier forms a virtual image.
Worked example
An object is 15 cm from a converging lens of focal length 10 cm. Using 1/f = 1/d_o + 1/d_i: 1/10 = 1/15 + 1/d_i, so 1/d_i = 1/30 and d_i = 30 cm. The image is real and on the opposite side. Magnification m = -30/15 = -2, so the image is twice as large and inverted. A ray parallel to the axis passes through the far focal point; a ray through the centre continues undeviated; their intersection confirms the result.
Traps
The most common error is mixing sign conventions. Keep object distances positive for real objects and interpret a negative image distance as virtual. Do not use sinθ ≈ θ unless the angle is small and the question allows it. Total internal reflection cannot occur going from air to glass. Magnification sign tells orientation, not simply size. For mirrors, the focal length is half the radius of curvature. Check whether the question asks for image position, size, orientation or nature; all four may be required.