Curved Mirrors & the Mirror Equation

You’ll be able to

Distinguish concave (converging) from convex (diverging) mirrors and their focal points
Use the mirror equation and sign conventions to locate an image
Predict whether an image is real or virtual, upright or inverted, enlarged or reduced

Concave and convex mirrors

A concave mirror curves inward like the inside of a bowl and converges parallel light to a focal point; its focal length f is positive. A convex mirror bulges outward and diverges light, so its rays only appear to come from a focal point behind the mirror; its focal length is negative. The focal length is half the radius of curvature: f = R/2. Concave mirrors can form either real or virtual images depending on where the object sits; convex mirrors always give one type of image.

Mirror equation and magnification

1/f = 1/d_o + 1/d_i · m = − d_i / d_o

Sign conventions: d_i is positive for a real image (in front of the mirror), negative for a virtual image (behind). A positive m is upright; negative m is inverted; |m| > 1 is enlarged.

Reading the signs

The signs in the mirror equation carry all the physics. A positive image distance (d_i > 0) means a real image, formed in front of the mirror where light actually converges — it can be projected on a screen and is inverted. A negative d_i means a virtual image behind the mirror, upright and impossible to project. The magnification m = −d_i/d_o then tells you the orientation and size in one number. Always solve the mirror equation first, then let the sign of d_i announce the image type.

Worked example

An object is placed 30 cm in front of a concave mirror with a focal length of 10 cm. Find the image distance and describe the image.

1.Mirror equation: 1/d_i = 1/f − 1/d_o = 1/10 − 1/30.
2.Common denominator: 1/d_i = 3/30 − 1/30 = 2/30 = 1/15.
3.Invert: d_i = 15 cm (positive → real image, in front of the mirror).
4.Magnification: m = −d_i/d_o = −15/30 = −0.5 (inverted and half the size).

Answer: d_i = 15 cm; the image is real, inverted, and reduced to half size (m = −0.5).

Checkpoint

An object is 30 cm in front of a concave mirror with focal length 10 cm. Where is the image?

Watch out

For a concave mirror f is positive; for a convex mirror f is negative. Plugging in the wrong sign for f flips the entire result. Decide the mirror type first, then assign the sign of f before you compute.

Checkpoint

A convex (diverging) mirror forms an image of a real object that is always:

On the exam

Convex mirrors and diverging lenses share a signature: they always make virtual, upright, diminished images, no matter where the object is. Concave mirrors and converging lenses are the versatile ones whose image type depends on object position.

Answer the 2 checkpoints as you read.