Refraction at a spherical surfaceगोलीय पृष्ठ पर अपवर्तनRefraction at a spherical surface

NCERT Fig 9.15 · Class 12 Physics · Chapter 9 · interactive diagram

Parts and what they mean

• Convex spherical surface of glass (काँच का उत्तल गोलीय पृष्ठ) — Separates medium n₁ (left) from n₂ (right). Its centre of curvature C is on the right, so R is positive.
• Principal axis (मुख्य अक्ष) — Through M (pole of the surface) and C.
• Incident ray ON (आपतित किरण ON) — From the object point O to the point N on the surface.
• Refracted ray NI (अपवर्तित किरण NI) — Bends towards the normal (n₂ > n₁) and crosses the axis at the image I. Traced with Snell’s law n₁ sin i = n₂ sin r.
• Normal at N (line CN) (N पर अभिलंब (रेखा CN)) — For a spherical surface the normal passes through the centre of curvature.
• Angle of incidence i (आपतन कोण i) — Exterior angle of triangle NOC: i = ∠NOM + ∠NCM ≈ MN/OM + MN/MC.
• Angle of refraction r (अपवर्तन कोण r) — r = ∠NCM − ∠NIM ≈ MN/MC − MN/MI.
• Object O (वस्तु O) — OM = −u.
• Pole M (ध्रुव M) — Distances are measured from here.
• Centre of curvature C (वक्रता केंद्र C) — MC = +R.
• Image I (प्रतिबिंब I) — MI = +v (real image inside the glass).
• Point of incidence N (आपतन बिंदु N) — Close to M for paraxial rays.
• Medium 1, index n₁ (माध्यम 1, अपवर्तनांक n₁) — Light starts here.
• Medium 2, index n₂ (माध्यम 2, अपवर्तनांक n₂) — n₂ > n₁ here.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 9.15. Report a mistake