Power of a lens

In a nutshell

Lenses change the direction of light rays to converge or diverge. They are used to form real or virtual images. The power of a lens is a measure of its ability to refract light.

Definitions

Keyword	Definition
Converge	Meet at a single point.
Diverge	Spread out - appears as if coming from a single point.
Axis	Line passing horizontally through the middle of the lens.
Principal focus / focal point	The focal point for a lens. A lens has a principal focus on each side.
Focal length	The distance from the centre of the lens to the principal focus/ focal point.
Object	What the light passing through the lens comes from.
Real image	Light meets at a point (converges) to form an image on a screen.
Virtual image	Light appears to be coming from a point (diverges) and forms an image not really there.

Equations

DESCRIPTION	EQUATION
Power of a lens	$P = \dfrac{1}{f}$

Variable definitions

QUANTITY NAME	SYMBOL	UNIT SYMBOL
$power \ of \ a \ lens$	$P$	$D$ or $m^{-1}$
$focal \ length$	$f$	$m$

Types of lenses

A lens is a specifically shaped piece of glass that refracts light rays when they pass through it. Lenses refract light rays so that they change direction. This makes objects appear differently to what they actually are.

There are two types of lenses: converging and diverging.

Converging lens

A converging lens bulges outwards towards the middle. This lens causes light parallel to the axis to converge at the focal point. The focal length is the distance from this focal point to the centre of the lens.

Physics; Lenses; KS5 Year 12; Power of a lens

1.	Focal Point

Diverging lens

A diverging lens bends inwards towards the middle. This lens causes light rays parallel to the axis to diverge. For a diverging lens, the focal point is where the rays diverging appear to have come from. The focal length is the distance from this focal point to the centre of the lens.

Physics; Lenses; KS5 Year 12; Power of a lens

1.	Focal Point

Power of a lens

If a lens has a shorter focal length, it is said to be more powerful, as shown by the equation:

$P = \dfrac{1}{f}$

Note: for a diverging lens, where the focal length is negative, power has a negative value.

The power of a lens is a measure of its ability to refract light. It also tells you how strongly the lens can focus the light. The unit of power of a lens is the dioptre ( $D$ ).

Example

A lens is set up between a bulb and a screen. The image of the bulb is in focus when the lens is $45 \ cm$ from the screen. Calculate the power of the lens.

State the variables from the question:

$f = 45 \ cm$

State the equation needed:

$P = \dfrac{1}{f}$

Substitute into the equation and solve:

$P = \dfrac{1}{45 \times 10^{-2}}\newline \\[0.1in] P = 2.222 \ D\newline \\[0.1in] P = 2.2 \ D \ \ (2sf)$

The power of the lens is $\underline{2.2 \ D}$ .