Reflection and Mirrors

The law of reflection states that when light bounces off a surface, the angle of reflection equals the angle of incidence, both measured from the normal to the surface:

$\theta_r = \theta_i$

Spherical Mirrors

A spherical mirror has a focal point $F$ at half the radius of curvature $R$:

$f = \frac{R}{2}$

• Concave mirror (converging): $f > 0$. Used in telescopes, headlights, and shaving mirrors.
• Convex mirror (diverging): $f < 0$. Used in security mirrors and car rear-view mirrors.

The Mirror Equation

The relationship between object distance $d_o$, image distance $d_i$, and focal length $f$:

$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$

Solving for the image distance:

$d_i = \frac{1}{\dfrac{1}{f} - \dfrac{1}{d_o}}$

Sign Conventions

Magnification

The lateral magnification relates image size to object size:

$m = -\frac{d_i}{d_o}$

• $|m| > 1$: image is magnified
• $|m| < 1$: image is diminished
• $m > 0$: image is upright (virtual)
• $m < 0$: image is inverted (real)

Your Task

Implement the mirror equation and magnification formula below.