What is the critical angle for a diamond (\( n = 2.42 \)) to water (\( n = 1.33 \)) interface?
**Spherical refracting surface** power P = (n₂-n₁)/R, lens power sum of two surfaces. Lens maker derivation combines two refractions, sign of R₂ negative for second surface convex opposite direction, yielding 1/f positive for convex lens. Critical angle: sin i_c = (n₂/n₁) . Diamond ( n₁ = 2.42 ), water ( n₂ = 1.33 ). sin i_c = (1.33/2.42) ≈ 0.55 . i_c = sin⁻¹(0.55) ≈ 33.4° . Substituting values gives 33°, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u (mirror), confirming sign conventions and refraction principles.
Ref: NCERT > Physics Book > Ray Optics > Refraction at Spherical Surfaces and Lens Maker's Formula