Reflection At Spherical Mirrors

Question

A convex mirror mounted on a delivery van has a radius of curvature of 3.0 m, so what is its focal length as felt by rays parallel to the axis?

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According to NCERT, for a spherical mirror the focal length equals half the radius of curvature, expressed as $f=\frac{R}{2}$, and this relation holds for paraxial rays close to the principal axis. A convex mirror has its centre of curvature and focus behind the reflecting surface, so under the Cartesian sign convention both are taken as positive when light travels from left to right. Substituting the radius $R=3.0$ m gives $f=\frac{3.0}{2}=1.5$ m, and the positive sign confirms the focus is virtual and located behind the mirror. The value $-1.5$ m is wrong because a convex mirror never has a real focus in front of it, so the sign must be positive. The value $+3.0$ m is wrong because it forgets to halve the radius, confusing $R$ with $f$. The value $-0.75$ m is wrong because it both halves twice and applies the wrong sign. As stated in NCERT Class 12, Chapter 9, convex mirrors always produce virtual, erect, diminished images, which is why they are used for wide-angle rear views. A magnitude check confirms a 3 m radius sensibly yields a 1.5 m focal length, half as large, matching the geometry.

Reflection At Spherical Mirrors

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