An object is 30 cm from a convex lens with f = 20 cm. Where does the image form?

You can work it out this way: apply 1/f = 1/v + 1/u with u = 30 and f = 20.

Under what condition does a convex lens produce a virtual image?

You can work it out this way: compare the object distance to the focal length.

An object is placed at 2f from a convex lens. Calculate the magnification.

You can work it out this way: find image distance first, then use m = -v/u.

Pro 🔒~25 min

Geometric Optics — Lenses & Mirrors

Trace rays through lenses and discover image formation

How it works

Geometric optics models light as rays that travel in straight lines and bend at interfaces according to Snell's Law. A thin lens refracts parallel rays to converge at (convex) or diverge from (concave) the focal point. The thin lens equation 1/f = 1/v + 1/u relates the focal length, image distance, and object distance, while the magnification m = -v/u describes image size and orientation.

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Step-by-step

Set the focal length with the slider — positive values give a convex lens, negative values a concave lens.
Move the object distance slider and observe how the image position and magnification change in real time.
Switch to Pro mode to change object height and toggle lens type explicitly.

Key formulas

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ Thin Lens Equation
$m = -\frac{v}{u}$ Magnification
$v > 0 \Rightarrow \text{Real image},\quad v < 0 \Rightarrow \text{Virtual image}$ Image type by sign of image distance

Frequently asked questions

An object is 30 cm from a convex lens with f = 20 cm. Where does the image form?: You can work it out this way: apply 1/f = 1/v + 1/u with u = 30 and f = 20.
Under what condition does a convex lens produce a virtual image?: You can work it out this way: compare the object distance to the focal length.
An object is placed at 2f from a convex lens. Calculate the magnification.: You can work it out this way: find image distance first, then use m = -v/u.