Lenses & Mirrors
Where does the image appear, and how big is it? The thin-lens and mirror equation for converging and diverging lenses and for concave and convex mirrors, with the three standard rays drawn one by one.
Real and Virtual Images
A real image is where light rays really come together: you can catch it on a screen, as in a camera or a projector. It is always upside down. A virtual image is where the rays only seem to come from: you see it by looking into the lens or mirror, like your face in a make-up mirror or a stamp under a magnifying glass. It cannot be caught on a screen.
Every point of an object sends rays in all directions; three of them are easy to follow, and two are already enough to find the image.
Ray Diagram, Step by Step
imageKey Relations
The same equation for lenses and mirrors. Sign rule used here: f > 0 for converging lenses and concave mirrors, f < 0 for diverging lenses and convex mirrors; di > 0 is a real image.
Negative m means an upside-down image; |m| > 1 means it is larger than the object.
Glasses are specified in dioptres: −2.5 D is a diverging lens with f = −40 cm. A spherical mirror has its focal point halfway to its centre of curvature.
Sources & Verification
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 34 (Images: spherical mirrors, thin lenses, ray diagrams).
- E. Hecht, Optics, 5th ed., Pearson, 2017 — Ch. 5 (Geometrical Optics).
Frequently Asked Questions
How do you use the thin lens equation?
1/f = 1/do + 1/di, with f the focal length, do the object distance and di the image distance. Solved for the image: di = f·do/(do − f). For a lens with f = 10 cm and an object at 30 cm: di = 10·30/20 = 15 cm, a real image on the other side. The same equation works for spherical mirrors.
How do you calculate magnification?
m = −di/do, and the image height is m times the object height. In the example above m = −15/30 = −0.5: the image is half as tall and upside down. A positive m means an upright image, |m| > 1 an enlarged one.
What is the difference between a real and a virtual image?
A real image is where the light rays really meet: it can be caught on a screen and is upside down, as in a camera or projector. A virtual image is where the rays only seem to come from: you see it by looking through the lens or into the mirror, like with a magnifying glass or a make-up mirror. In the equation a real image has a positive di, a virtual image a negative one.
How does a magnifying glass work?
Hold the object closer to a converging lens than its focal length. The rays then spread out after the lens, and your eye sees them coming from a larger, upright virtual image further away. With f = 10 cm and the object at 6 cm, the image is at −15 cm and 2.5 times as large.
What are the three principal rays in a ray diagram?
1. A ray parallel to the axis goes through the focal point after the lens (or after reflecting from a concave mirror). 2. A ray through the centre of a lens goes straight on; a ray hitting the middle of a mirror reflects at the same angle. 3. A ray through the focal point comes out parallel to the axis. Where these rays, or their backward extensions, meet is the image.
What is optical power in dioptres?
The inverse of the focal length in metres: P = 1/f. A lens with f = 50 cm has +2 dioptres; glasses for short-sightedness use diverging lenses with a negative power, for example −2.5 D for f = −40 cm. The stronger the lens, the larger the number.