Spherical MirrorsJEE Main

Concept

A spherical mirror forms images by reflection. A concave mirror converges light and can make real or virtual images depending on where the object sits; a convex mirror always diverges light into a virtual, erect, diminished image.

Key formula

Derivation

With the Cartesian convention (distances from the pole, incident direction positive) the object distance is $u<0$; a concave mirror has $f<0$.

Two principal rays fix the image: a ray parallel to the axis reflects through the focus $F$; a ray through the centre of curvature $C$ retraces its path. Their meeting point is the image tip.

Algebra gives $\tfrac1v + \tfrac1u = \tfrac1f$ with $f = R/2$, and magnification $m = -v/u$. A negative $m$ is an inverted (real) image.

Scenarios to explore

• Spherical Mirrors — Concave & convex mirror image formation.

Real-world applications

• Vehicle headlights and torches (concave reflectors).
• Rear-view and security mirrors (convex, wide field of view).
• Reflecting telescopes and shaving/make-up mirrors.

JEE exam tips

• Object between pole and focus of a concave mirror → virtual, erect, magnified image.
• Focal length is half the radius of curvature: $f = R/2$.

Common mistakes

• Forgetting that a concave mirror has a negative focal length in this convention.
• Using the magnification sign $m = +v/u$ (the mirror formula has a minus).
• Assuming a convex mirror can ever produce a real image (it cannot).

Exam traps to avoid

• A concave mirror makes a virtual image only when the object is inside the focal length.
• Convex mirror magnification is always between 0 and 1 (diminished, erect).