Lenses & Ray Diagrams for Telescopes (AQA A Level Physics): Revision Note

Lenses & ray diagrams for telescopes

• 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

• Note: in the Astrophysics module, only converging lenses will be discussed

• 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 distance from the centre of the lens to the focal point is called the focal length

  • 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

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:

The lens equation & magnification

The lens equation

• The lens equation relates the focal length of a lens to the distances between the lens and the image and the object

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

• Where:

  • $f$ = focal length (m)

  • $v$ = distance of the image from lens (m)

  • $u$ = distance of the object from lens (m)

Lens equation for a real image

• This equation only works for thin converging (or diverging) lenses

  • If the image is real, the value of $v$ is positive 

  • If the image is virtual, the value of $v$ is negative

Lens equation for a virtual image

Magnification as a ratio of heights

• Magnification, $M$, is the ratio of the image height to the object height

$M=\frac{h_i}{h_o}$

• Where:

  • $M$ = magnification

  • $h_i$ = image height (m)

  • $h_o$ = object height (m)

Magnification as a ratio of distances

• A diagram of an object and its real image will produce similar triangles

• Therefore, magnification can be determined by comparing the distances from the lens to the object and the image

Magnification ray diagram for a real image

• This also works for virtual images

Magnification ray diagram for a virtual image

• As magnification can be described using the ratio of the two opposite sides $h_i$ and $h_o$, the same ratio must apply to the two adjacent sides $v$ and $u$

• Therefore, magnification can also be written as:

 $M=\frac{v}{u}$

• Where:

  • $M$ = magnification

  • $v$ = distance from lens to image (m)

  • $u$ = distance from lens to object (m)

• Since magnification is a ratio, it has no units