Cameras, magnifying glasses and spectacles all rely on lenses. Learn how a lens makes an image and how its power is measured.
A convex lens is thicker at the centre and converges light, while a concave lens is thinner at the centre and diverges light. The principal focus F is where rays parallel to the axis meet (or appear to come from), and the focal length f is its distance from the optical centre O. To draw an image from a convex lens, use two rays: one parallel to the axis, which passes through the focus, and one through the optical centre, which goes straight on.
Which ray goes straight through a lens without bending?
The ray through the optical centre
What happens to a ray parallel to the principal axis after passing through a convex lens?
It bends and passes through the principal focus on the other side
Object beyond 2F: image between F and 2F, real, inverted, diminished. Object at 2F: image at 2F, real, inverted, same size. Object between F and 2F: image beyond 2F, real, inverted, magnified. Object at F: image at infinity. Object between O and F: image on the same side, virtual, erect, magnified. A concave lens always forms a virtual, erect, diminished image between F and O.
Where must an object be placed for a convex lens to act as a magnifying glass, and what is the image like?
Between the optical centre and the focus; the image is virtual, erect and magnified
An object stands beyond 2F of a convex lens. Describe the image.
It is formed between F and 2F on the other side, and is real, inverted and diminished (as in a camera)
Describe the image formed by a concave lens.
It is always virtual, erect and diminished, and lies between the lens and its focus
The power of a lens is the reciprocal of its focal length in metres, P = 1 ÷ f, measured in dioptres (D). A convex lens has positive power and a concave lens has negative power. The powers of lenses in contact add up.
Find the power of a convex lens of focal length 25 cm.
f = 0.25 m, so P = 1 ÷ 0.25 = +4 D
Find the power of a concave lens of focal length 50 cm.
f = 0.5 m, so P = 1 ÷ (−0.5) = -2 D
A +4 D lens and a −2 D lens are placed in contact. Find the power and focal length of the combination.
P = +4 + (−2) = +2 D, and f = 1 ÷ 2 = 0.5 m = 50 cm
1. Define the principal focus of a convex lens.
2. Which type of lens is a converging lens?
3. Describe the image when an object is placed at 2F of a convex lens.
4. When is a convex lens used as a magnifying glass?
5. Describe the image formed by a concave lens.
6. Find the power of a convex lens of focal length 25 cm.
7. Find the power of a concave lens of focal length 50 cm.
8. Find the power of a +4 D lens and a −2 D lens in contact.
9. What is the unit of the power of a lens?
10. Name an instrument in which a convex lens forms a real, inverted, diminished image.