Converging & Diverging Lenses (AQA A Level Physics): Revision Note

Converging lenses

• A lens is a piece of equipment that forms an image by refracting light

• There are two types of lenses: 

  • a convex, or converging lens

  • a concave, or diverging lens

• In a converging lens, parallel rays of light are brought to a focus along the principal axis

  • This point is called the focal point

The ray diagram of a converging lens

• The distance from the centre of the lens to the focal point is called the focal length, $f$

  • This length depends on how curved, or how thick, the lens is

  • The more curved (thicker) the lens, the shorter the focal length

  • The shorter the focal length, the more powerful the lens

  • $f$ is positive for a converging lens because it is in front of the lens

The different shapes of lenses with long and short focal lengths

Real and virtual images

• Images produced by lenses can be either real or virtual

Real image	Virtual image
Light converges towards a focal point	Light diverges away from a focal point
Always inverted	Always upright
Can be projected onto a screen	Cannot be projected onto a screen
Intersection of two solid lines	Intersection of two dashed lines (or a dashed and a solid line)

Constructing ray diagrams

• When constructing ray diagrams of refractors, it is generally assumed that the lenses used are very thin

  • This simplifies the situation by reducing the amount the incident rays of light refract

• As a result, the three main rules for constructing ray diagrams are as follows:

1. Rays passing through the principal axis will pass through the optical centre of the lens undeviated

2. Rays that are parallel to the principal axis will be refracted and pass through the focal point $f$

3. Rays passing through the focal point $f$ will emerge parallel to the principal axis

Image formation by a converging lens

• Images formed by lenses can be described by their:

  • nature: Real or virtual

  • orientation: Inverted or upright (compared to the object)

  • size: Magnified (larger), diminished (smaller), or the same size (compared to the object)

Drawing ray diagrams of real images

• For an object placed at a distance greater than two focal lengths...

• The image that forms will have the following properties:

• For an object placed at a distance equal to two focal lengths...

• The image that forms will have the following properties:

• For an object placed at a distance between one and two focal lengths

• The image that forms will have the following properties:

Drawing ray diagrams of virtual images

• For an object placed at a distance less than the focal length (i.e. a magnifying glass):

• The image that forms will have the following properties:

Diverging lenses

• In a diverging lens, parallel rays of light are made to diverge (spread out) from the principal focus on the principal axis

  • This lens is sometimes referred to as a concave lens

Ray diagram for a diverging lens

• Just like for converging lenses, the distance from the centre of the lens to the focal point is called the focal length, $f$

  • This length also depends on how curved, or how thick, the lens is

  • The more curved (thicker) the lens, the shorter the focal length

  • The shorter the focal length, the more powerful the lens

  • However, $f$ is negative for a diverging lens because it is behind the lens

Image formation by a diverging lens

• No matter the position of the object, all images formed by diverging lenses have the following properties:

  • Nature: Virtual (and not real)

  • Orientation: Upright (the same as the object)

  • Size: Diminished (smaller than the object)

  • Position: On the same side of the lens as the object

• For an object placed at any distance away from the lens (further than the focal point or closer than):

  • the ray of light incident on the centre of the lens does not change direction

  • the rays of light parallel to the principal axis are refracted

    • It appears that they come from a virtual focus 

Virtual image produced by a diverging lens for an object beyond f

Virtual image produced by a diverging lens for an object closer than f

Constructing ray diagrams for diverging lenses

• Follow the steps below to produce a ray diagram for a diverging lens:

Virtual image produced by a diverging lens

1. Start by drawing a ray going from the top of the object through the centre of the lens. This ray will continue to travel in a straight line.

2. Next, draw a ray going from the top of the object, travelling parallel to the axis to the lens. When this ray emerges from the lens, it will move in a line as if coming from the focal point.

3. Draw a dashed line continuing this ray downwards to the focal point, $f$.

4. The image is the line drawn from the axis to the point where the above two rays meet.