10.1.1 Converging & Diverging 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

A converging lens brings parallel rays of light to a focus

• 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

The focal length is shorter in a lens that is thicker and more curved. This makes for a more powerful lens

Real & 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)
example: image from a projector onto a screen	example: image in a mirror

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

 

Converging Lens Ray Diagram Construction Rule 1

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

 

Converging Lens Ray Diagram Construction Rule 2

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

 

Converging Lens Ray Diagram Construction Rule 3

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 2 focal lengths...

 

A Converging Lens Ray Diagram for an Object Placed Further than 2f

• The image that forms will have the following properties:

The image forms...	between f and 2f
The nature of the image is...	real
The orientation of the image is...	inverted
The size of the image is...	diminished

 

• For an object placed at a distance equal to 2 focal lengths...

 

A Converging Lens Ray Diagram for an Object Placed at 2f

• The image that forms will have the following properties:

The image forms...	at 2f
The nature of the image is...	real
The orientation of the image is...	inverted
The size of the image is...	the same

 

• For an object placed at a distance between 1 and 2 focal lengths

 

A Converging Lens Ray Diagram for an Object Placed Between f and 2f

• The image that forms will have the following properties:

The image forms...	beyond 2f
The nature of the image is...	real
The orientation of the image is...	inverted
The size of the image is...	magnified

 

Drawing ray diagrams of virtual images

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

 

A Converging Lens Ray Diagram for an Object Placed Less than f

• The image that forms will have the following properties:

The image forms...	at 2f (on the same side as the object)
The nature of the image is...	virtual
The orientation of the image is...	upright
The size of the image is...	magnified

• 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

The Ray Diagram of a Diverging Lens

Parallel rays from a diverging lens appear to come from the principal focus

• 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 are:
  • 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 with Object Beyond f

A diverging lens always produces a virtual image no matter the position of the object in relation to the focal point or the lens. Here the object is further away from the lens than the focal point.

 

  

Virtual Image Produced by a Diverging Lens with Object Closer than f

A diverging lens always produces a virtual image no matter the position of the object in relation to the focal point or the lens. Here the object is closer to the lens than the focal point.

Constructing Ray Diagrams for Diverging Lenses

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

Step By Step To Constructing a Virtual Image from a Diverging Lens

The step-by-step procedure for drawing accurate diverging lens ray diagrams

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