Thin Lens Equation

A thin lens is one whose thickness is negligible compared to the other distances involved. Lenses work by refracting light at two curved surfaces.

Types of Lenses

• Converging (convex) lens: thicker at the center; $f > 0$. Focuses parallel rays to a real focal point.
• Diverging (concave) lens: thinner at the center; $f < 0$. Spreads rays as if from a virtual focal point.

The Thin Lens Equation

The same form as the mirror equation:

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

Solving for image distance:

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

Sign Convention

Magnification

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

Lens Power

Optometrists measure lens strength in diopters (D), which is simply the reciprocal of the focal length in meters:

$P = \frac{1}{f_{\text{meters}}}$

A +2 D lens has $f = 0.5\,\text{m}$; a −4 D lens has $f = −0.25\,\text{m}$.

Ray Diagrams

Three principal rays for a converging lens:

1. A ray parallel to the axis refracts through the far focal point.
2. A ray through the optical center passes straight through.
3. A ray through the near focal point emerges parallel to the axis.

Your Task

Implement the three functions below.