Mirrors and Lenses - Physics Q and A

« Back to AP Physics Guide / Unit 13: Geometric Optics / 13.2 & 13.4: Mirrors & Lenses

A glowing conceptual visualization of a converging lens focusing light rays from a candle to form a sharp, inverted image on a screen.

Optics goes beyond bending light; it’s about predicting where light will converge to form an image.

Now that we know how light reflects and refracts at a single boundary, we can use curved surfaces to manipulate light in useful ways. Curved mirrors (Topic 13.2) rely on reflection, while lenses (Topic 13.4) rely on refraction. Remarkably, the math used to predict images for both is exactly the same!

1. Spherical Mirrors (Topic 13.2)

Mirrors that curve inward like a cave are Concave (converging). Mirrors that bulge outward are Convex (diverging). The most important feature of any curved mirror or lens is its Focal Length ( $f$ ).

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

For a spherical mirror, the focal length ( $f$ ) is exactly half of its radius of curvature ( $R$ ).

Diagram showing parallel light rays striking a concave mirror and converging at the focal point (f), and rays striking a convex mirror and diverging.

Concave mirrors focus parallel rays to a real focal point. Convex mirrors scatter them from a virtual focal point.

2. Thin Lenses (Topic 13.4)

Lenses work by refracting light twice (entering and exiting the glass). A Converging Lens (convex shape, thicker in the middle) forces light rays together. A Diverging Lens (concave shape, thinner in the middle) spreads them apart.

Concept First: The shape names flip, but the functions don’t! A concave mirror converges light. A convex lens converges light. Remember the function (Converging/Diverging) rather than memorizing the shape name!

3. The Lens / Mirror Equation

Whether you are dealing with a mirror or a lens, the location and size of the image are governed by two fundamental equations:

$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \quad \text{and} \quad M = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$

Where $f$ is focal length, $d_o$ is object distance, $d_i$ is image distance, and $M$ is magnification.

Positive $d_i$ : The image is Real (can be projected on a screen) and will be inverted.
Negative $d_i$ : The image is Virtual (looks like it’s “inside” the mirror/lens) and will be upright.
Negative $M$ : The image is inverted.

⚙️ Interactive Convex Lens Simulator

Drag the object (blue arrow) toward the lens. Watch what happens to the image (red arrow) when the object crosses the focal point ( $f$ )!

Object Distance ( $d_o$ ): 150 cm

Image Distance ( $d_i$ ): 0 cm

Magnification ( $M$ ): 0x

Image Type: Real

Orientation: Inverted

4. Quick AP Practice

📚 Unit 13 Mastery Challenge

1. An object is placed 15 cm in front of a converging lens with a focal length of 10 cm. Will the image be real or virtual?

Check Answer

Using the equation: $\frac{1}{10} = \frac{1}{15} + \frac{1}{d_i}$
$\frac{1}{d_i} = \frac{3}{30} - \frac{2}{30} = \frac{1}{30}$
$d_i = +30$ cm. Because $d_i$ is positive, the image is Real (and inverted).

2. You look into a shiny, spherical Christmas ornament (a convex mirror). Why does your reflection always look smaller?