Practice question

**Critical angle** C satisfies sinC = n₂/n₁, n₁>n₂, n₂=1 for air, n₁=1.52 for glass gives sinC=1/1.52=0.6579, C≈41.1°, for water n=1.33 C=48.75°. Beyond C, total internal reflection occurs, all light reflected, no refracted ray, used in optical fibers and prisms. Focal length: f = (R/2) = (-20/2) = -10 cm (concave mirror). Image distance: v = -20 cm (real image). Mirror equation: (1/v) + (1/u) = (1/f) . (1/-20) + (1/u) = (1/-10) ⇒ (1/u) = (1/-10) + (1/20) = (-2 + 1/20) = (-1/20) . u = -20 cm . Substituting values gives 20 cm, which matches expected image position and magnification from mirror/lens formula