Practice question

**Lens maker's formula** 1/f = (n-1)(1/R₁ - 1/R₂), n refractive index, R₁,R₂ radii of curvature (m), sign convention R positive if surface convex towards incident light. For double convex R₁=12 cm, R₂=-12 cm, n=1.5, 1/f=(0.5)(1/12 -1/(-12))=(0.5)(2/12)=1/12, f=12 cm, converging. Total internal reflection occurs when light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle. The critical angle depends on the refractive indices of the two media, making the angle of incidence the decisive factor for the phenomenon. Substituting values gives Angle of incidence relative to the critical angle, which matches expected image position and magnification from mirror/lens