Two kinds of lens
A convex (converging) lens is thicker in the middle and bends parallel rays together to a real focal point. A concave (diverging) lens is thinner in the middle and spreads parallel rays apart; the rays appear to come from a virtual focal point. The distance from the lens centre to the principal focus is the focal length, f.
Drawing ray diagrams
To locate an image from a convex lens, draw any two of these standard rays from the top of the object:
- A ray parallel to the principal axis refracts through the far focal point F.
- A ray through the optical centre passes straight on without bending.
- A ray through the near focal point F refracts parallel to the axis.
Where the rays cross is the top of the image. An image can be described by four features: real or virtual, upright or inverted, magnified or diminished, and its position.
Remember / Remember
- Object beyond 2F: image is real, inverted, diminished (used in a camera).
- Object between F and 2F: image is real, inverted, magnified (projector).
- Object inside F: image is virtual, upright, magnified (magnifying glass).
- A concave lens always gives a virtual, upright, diminished image.
Key formula / Key formula
Linear magnification: m = image height / object height = v / u
If m > 1 the image is magnified; if m < 1 it is diminished.
Worked example / Worked example
An object 3.0 cm tall is placed in front of a convex lens and produces a real image 30 cm from the lens where the object is 15 cm from the lens. Find the magnification and image height.
m = v / u = 30 / 15 = 2.0.
Image height = m × object height = 2.0 × 3.0 = 6.0 cm, inverted.