Two kinds of spherical mirror
A concave (converging) mirror curves inward and reflects parallel rays to a real focal point in front of it. A convex (diverging) mirror curves outward and spreads parallel rays apart so they appear to come from a virtual focus behind it. The focal length f is half the radius of curvature R.
Key formula / Key formula
f = R / 2
Mirror equation: 1/f = 1/u + 1/v. Magnification: m = v / u.
Concave mirror f is positive; convex mirror f is negative.
Images in a concave mirror
- Object beyond C (centre of curvature): real, inverted, diminished.
- Object between C and F: real, inverted, magnified.
- Object inside F: virtual, upright, magnified (a shaving/make-up mirror).
Images in a convex mirror
A convex mirror always forms a virtual, upright, diminished image, whatever the object distance. Its wide field of view makes it useful as a car wing mirror and a shop security mirror.
Worked example / Worked example
An object is 30 cm in front of a concave mirror of radius of curvature 20 cm. Find the image distance and magnification.
f = R/2 = 20/2 = 10 cm.
1/v = 1/f − 1/u = 1/10 − 1/30 = (3 − 1)/30 = 2/30 = 1/15.
v = 15 cm (real).
m = v/u = 15/30 = 0.5 — a real, inverted, diminished image.
Remember / Remember
- f = R/2 for any spherical mirror.
- A convex mirror only ever gives a virtual, upright, diminished image.
- A concave mirror inside F gives an upright magnified image (shaving mirror).