Physics · Ray Optics And Optical Instruments · NEET
Yes. The relation f = R/2 holds for both mirror types. For a concave mirror, R is negative (centre C is in front, on the same side as the object), so f is also negative. For a convex mirror, R is positive (C is behind the mirror), so f is positive. The magnitude rule |f| = |R|/2 never changes; only the signs flip with the Cartesian sign convention.
A ray parallel to the principal axis hits the mirror at point M and reflects to cross the axis at focus F. The normal at M passes through the centre of curvature C, so the angle of incidence equals the angle CMF. By the law of reflection and alternate angles, triangle CMF is isosceles with CF = FM. For a small aperture (paraxial ray), M lies very close to the pole P, so FM is almost equal to FP = f and CP = R. Since F bisects CP, we get f = R/2.
Only for paraxial rays — rays close to and nearly parallel to the principal axis. For rays far from the axis (a wide aperture), reflected rays cross the axis at different points, causing spherical aberration, and there is no single sharp focus. NEET always assumes paraxial (small-aperture) mirrors, so you can safely use f = R/2 in every numerical.
Using the Cartesian sign convention with light travelling left to right, distances measured against the incident light are negative. For a concave mirror both C and F are in front (real side), so R and f are both negative. Example: a concave mirror of radius of curvature 20 cm has R = -20 cm and f = -10 cm. Watch out: many problems quote the magnitude, and you must attach the minus sign yourself.
No. f = R/2 is a mirror-only relation. Lenses have two surfaces with radii R1 and R2 and depend on the refractive index through the Lens Maker's Formula: 1/f = (n-1)(1/R1 - 1/R2). Never apply f = R/2 to a lens in NEET — it is a common trap.
Just double the focal length: R = 2f. If a concave mirror has f = -15 cm, then R = -30 cm. If a convex mirror has f = +25 cm, then R = +50 cm. Keep the sign of f and it carries over to R automatically.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
No. Mirror focal length depends only on geometry (reflection), not on the surrounding medium. A concave mirror has the same f in air, water, or oil. This is unlike a lens, whose focal length changes when immersed in a liquid because refraction depends on the relative refractive index.
A plane mirror is a spherical mirror with infinite radius of curvature (R = infinity). So f = R/2 = infinity. That is why a plane mirror cannot converge parallel rays to a real focus — its focus is at infinity, and it always forms a virtual, erect, same-size image.
Since f = R/2, the mirror with the smaller radius has the shorter focal length. The 30 cm mirror has f = 15 cm and the 60 cm mirror has f = 30 cm. A shorter focal length means a more strongly curved, more converging (or diverging) mirror.
Yes. First convert the given radius to focal length using f = R/2 (keeping the correct sign), then plug f into the mirror formula 1/v + 1/u = 1/f. NEET numericals often give R and expect you to make this conversion in the first step.
