Lenses

(Separate Physics only) This whole topic is assessed only in the separate GCSE Physics course, not in Combined Science.

A lens is a shaped piece of transparent material that forms an image by refracting (bending) light. There are two types, defined by their shape and by what they do to parallel rays of light.

A convex lens is thicker in the middle than at the edges. It is also called a converging lens because it brings parallel rays of light together to a point.

A concave lens is thinner in the middle than at the edges. It is also called a diverging lens because it spreads parallel rays of light apart.

Lens type	Shape	Effect on parallel rays	Standard symbol
Convex (converging)	Thicker in the middle	Rays converge to a point	An upright line with an arrowhead at each end pointing outward
Concave (diverging)	Thinner in the middle	Rays diverge apart	An upright line with an arrowhead at each end pointing inward

Every image in this topic is produced by the refraction of light as it passes into and out of the lens.

(Separate Physics only)

When rays travelling parallel to the principal axis (the horizontal line through the centre of the lens) pass through a convex lens, they are refracted so that they all meet at a single point on the axis. This point is the principal focus (or focal point).

For a concave lens, the parallel rays are spread apart. If you trace the diverging rays straight backwards, they appear to come from a single point on the axis in front of the lens. That point is the principal focus of a concave lens.

Focal length is the distance from the centre of the lens to the principal focus.

A lens has a principal focus on both sides, the same distance from the lens, because light can enter from either direction.

The more strongly a lens bends light, the closer to the lens the rays meet, so a more powerful lens has a shorter focal length. A fat convex lens has a short focal length; a thin one has a long focal length.

The focal length is fixed by the lens itself. It does not depend on where you put the object.

(Separate Physics only)

To find where a convex lens forms an image, draw two rays from the top of the object and see where they cross. Two standard rays are enough:

1. A ray from the top of the object travelling parallel to the axis, which refracts through the principal focus on the far side.
2. A ray from the top of the object passing straight through the centre of the lens without bending.

Where these two rays cross is the top of the image. For an object placed beyond twice the focal length, the rays cross on the far side, forming a real, inverted, smaller image, which is how a camera works.

The image here is real because the two rays actually meet: you could place a screen there and see the image projected. It is upside down (inverted) compared with the object. Moving the object closer to the lens moves the image and changes its size.

Draw the ray from the tip of the object, mark the two principal foci at equal distances, and use a ruler. The image top sits where the rays cross.

(Separate Physics only)

Whether an image is real or virtual depends on the lens and, for a convex lens, on where the object is.

A real image forms where light rays actually meet. It can be projected onto a screen and is always inverted. A virtual image forms where rays only appear to come from; the rays never really meet, so it cannot be projected and is always upright.

• A convex lens forms a real image when the object is beyond the principal focus. When the object is closer than the focal length, the lens acts as a magnifying glass and forms a virtual, upright, enlarged image on the same side as the object.
• A concave lens always forms a virtual, upright, smaller image, whatever the object distance.

Lens	Object position	Image type
Convex	Beyond principal focus	Real, inverted
Convex	Closer than principal focus	Virtual, upright, enlarged (magnifying glass)
Concave	Any position	Virtual, upright, smaller

For a virtual image on a ray diagram, the refracted rays are traced backwards as dashed lines to the point they seem to come from.

(Separate Physics only)

Magnification tells you how much larger or smaller the image is than the object.

$\text{magnification}=\frac{\text{image height}}{\text{object height}}$

This equation is given on the Physics equation sheet. Magnification is a ratio, so it has no units. The image height and object height must both be in the same unit (both in mm, or both in cm).

A magnification greater than 1 means the image is larger than the object; less than 1 means it is smaller.

Worked example 1. An object is 5 mm tall. A convex lens forms an image 15 mm tall. Find the magnification.

$\text{magnification}=\frac{15\text{ mm}}{5\text{ mm}}=3$

The image is 3 times the height of the object.

Worked example 2. An object 8 cm tall gives an image 2 cm tall through a concave lens. Find the magnification, and find the image height for a different 6 cm object at the same magnification.

$\text{magnification}=\frac{2\text{ cm}}{8\text{ cm}}=0.25$

The magnification is 0.25, so the image is a quarter the size (the image is smaller, as expected for a concave lens). Rearranging, image height = magnification × object height:

$\text{image height}=0.25\times 6\text{ cm}=1.5\text{ cm}$

1. Confusing convex and concave

A convex lens is thicker in the middle and converges light; a concave lens is thinner in the middle and diverges light. Link the shape to the effect so the two do not get swapped.

2. Giving magnification a unit

Magnification is image height divided by object height, so the units cancel and it has no units. Writing "×3 cm" or "3 m" is wrong; the answer is just a number.

3. Mixing the two heights' units

Both heights must be in the same unit before dividing. If the object is in cm and the image is in mm, convert one first, or the ratio is meaningless.

4. Saying a concave lens can form a real image

A concave (diverging) lens always forms a virtual, upright, diminished image. Only a convex lens can form a real image, and only when the object is beyond the principal focus.

5. Forgetting to trace virtual-image rays backwards

For a virtual image, the refracted rays diverge and never meet in front of the lens. Extend them backwards as dashed lines to find where the image appears; do not look for a crossing point on the far side.