Why f = R/2 (geometry)f = R/2 क्यों (ज्यामिति)Why f = R/2 (geometry)

NCERT Fig 9.1, 9.4 · Class 12 Physics · Chapter 9 · interactive diagram

Parts and what they mean

• Concave mirror (अवतल दर्पण) — A reflecting surface that is part of a hollow sphere, silvered on the outside so it reflects from the inside (curved in towards the object). Converging.
• Principal axis (मुख्य अक्ष) — The line through the pole P and the centre of curvature C.
• Incident ray parallel to the axis (अक्ष के समांतर आपतित किरण) — Strikes the mirror at M.
• Reflected ray (परावर्तित किरण) — Angle of reflection = angle of incidence θ; the incident ray, normal and reflected ray lie in one plane. It crosses the axis at F.
• Normal CM (along the radius) (अभिलंब CM (त्रिज्या के अनुदिश)) — For a spherical mirror the normal at any point is the radius drawn from the centre of curvature C.
• Perpendicular MD (लंब MD) — Drop from M onto the axis: tan θ = MD/CD and tan 2θ = MD/FD.
• Angle of incidence θ (आपतन कोण θ) — Between the incident ray and the normal.
• Angle of reflection θ (परावर्तन कोण θ) — Between the normal and the reflected ray; equal to the angle of incidence.
• ∠MCP = θ (∠MCP = θ) — Alternate angles: the incident ray is parallel to the axis.
• ∠MFP = 2θ (∠MFP = 2θ) — Exterior angle of triangle MCF = θ + θ.
• Centre of curvature C (वक्रता केंद्र C) — Centre of the sphere of which the mirror is a part. PC = R. A ray through C hits the mirror along the normal and retraces its path.
• Principal focus F (मुख्य फोकस F) — Rays parallel to the axis meet here after reflection (concave) or seem to come from here (convex). PF = f = R/2.
• Pole P (ध्रुव P) — Geometric centre of the mirror surface. All distances are measured from P.
• Foot of perpendicular D (लंब का पाद D) — For paraxial rays D is very close to P, so FD ≈ f and CD ≈ R.
• Point of incidence M (आपतन बिंदु M) — Where the ray meets the mirror.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 9.1, 9.4. Report a mistake