Reflection and Mirrors

Light is an electromagnetic wave that travels in straight lines in a uniform medium. On reflection:

• The angle of incidence equals the angle of reflection — both measured from the normal (the line perpendicular to the surface), not from the surface itself.
• The incident ray, reflected ray, and normal all lie in one plane.

These laws hold for every mirror, flat or curved.

A plane mirror image is:

• Virtual (formed behind the mirror, cannot be projected on a screen),
• Erect (the same way up),
• Same size as the object,
• Laterally inverted (left ↔ right swapped),
• as far behind the mirror as the object is in front.

A periscope uses two plane mirrors and works purely by reflection. To see your full height you need a mirror only half your height, fixed at the right level — this is independent of how far you stand.

Key points on a spherical mirror: pole (P) — the centre of the reflecting surface; centre of curvature (C) — centre of the sphere it is cut from; focus (F) — the point where rays parallel to the axis converge (concave) or appear to diverge from (convex); radius of curvature (R) = PC.

• Relation: $R = 2f$, i.e. $f = R/2$.
• A concave mirror is converging; a convex mirror is diverging.
• A plane mirror is the limiting case $R \to \infty$, so $f \to \infty$ — which is why the mirror formula reduces to the plane-mirror equation there.

Concave-mirror image as the object moves in:

• Beyond C: real, inverted, diminished, between F and C.
• At C: real, inverted, same size, at C.
• Between C and F: real, inverted, magnified, beyond C.
• At F: image at infinity (used in headlights/searchlights — source at F gives a parallel beam).
• Between F and P: virtual, erect, magnified, behind the mirror.

An object exactly at the focus does NOT give an image between F and P — that combination is impossible.

For a convex mirror, for every real object position:

• the image is virtual,
• erect,
• diminished (smaller than the object),
• located between the pole P and the focus F, behind the mirror.

It can never form a real or inverted image. The wide field of view makes it ideal for rear-view mirrors and at blind corners.

Mirror formula: $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$, where distances follow the New Cartesian sign convention (measured from the pole; distances against the incident light are negative). Magnification: $m = \dfrac{h'}{h} = -\dfrac{v}{u}$.

• $m < 0$: real, inverted image. $m > 0$: virtual, erect image.
• $|m| > 1$: magnified; $|m| < 1$: diminished.

Concave mirror: $f$ is negative. Convex mirror: $f$ is positive.