Learning outcomes
- Use principal rays to construct converging-lens images.
- Distinguish real and virtual images.
- Predict image orientation, size and position for different object distances.
- Draw accurate diagrams with correct line conventions.
10.1 Principal rays
Three standard rays are used for a converging lens. A ray parallel to the principal axis refracts through the far focus. A ray through the optical centre continues straight. A ray directed through the near focus emerges parallel to the axis. Any two locate the image; a third can check accuracy.
For a real image, the refracted rays actually meet. Draw the image at their intersection. For a virtual image, refracted rays diverge and only their backward extensions meet. Draw these extensions as dashed lines.
10.2 Object beyond twice the focal length
When the object is beyond 2F, the image forms between F and 2F on the opposite side. It is real, inverted and smaller than the object. Cameras use a similar arrangement for distant scenes, although their sensors and focusing systems are more complex.
As the object moves very far away, the image approaches the focal plane and becomes very small. This links with the distant-object method for estimating focal length.
10.3 Object at 2F
When the object is at 2F, the image forms at 2F on the opposite side. It is real, inverted and the same size. The diagram is symmetrical about the lens if drawn accurately.
This case is useful for checking a ray construction because equal object and image distances and equal heights should appear on the diagram.
10.4 Object between F and 2F
The image forms beyond 2F. It is real, inverted and enlarged. Projectors use an object slightly beyond the focal point to produce a large real image on a distant screen.
As the object approaches F from outside, the image distance and magnification increase. At exactly F, the emerging rays are parallel and no image is formed at a finite screen distance.
10.5 Object inside F
When the object is closer to a converging lens than F, the refracted rays diverge. Their backward extensions form an image on the same side as the object. The image is virtual, upright and enlarged. This is the magnifying-glass arrangement.
Because the image is virtual, it cannot be projected onto a screen. The observer looks through the lens and sees rays that appear to come from the enlarged image.
10.6 Diverging-lens images
A diverging lens forms a virtual, upright and diminished image for a real object at any ordinary position. Draw one ray through the optical centre and one parallel ray that refracts as if from the near focus. Their backward extensions locate the image between the lens and focus.
The current syllabus emphasises the action of diverging lenses and their use in correcting short sight. A clear qualitative diagram is more important than numerical calculation.
Worked examples
Image classification
An object is placed 1.5 focal lengths from a converging lens. It lies between F and 2F, so the image is beyond 2F, real, inverted and enlarged.
Screen test
A sharp image appears on a screen. Because actual rays reach the screen and converge there, the image is real.
Practical focus
Investigation
Use an illuminated object, converging lens and screen on a metre rule. Find image positions for an object beyond 2F, at about 2F and between F and 2F. Record orientation, size and whether the image can be focused on the screen.
Examination guidance
- Ray diagrams should be large, ruled and labelled.
- Do not continue a ray undeviated unless it passes through the optical centre.
- A virtual image is located using dashed backward extensions, not by drawing actual rays behind the lens.
Check your understanding
- Describe the image when the object is between F and 2F.
- Which image type can be projected?
- What happens when an object is inside F of a converging lens?
Answers
- Real, inverted, enlarged and beyond 2F.
- A real image.
- A virtual, upright, enlarged image forms on the object side.
