Topic 5 of 5
Real and virtual images
To classify an image, follow the rays first. Then compare the image's orientation and height with the object's.
A thin converging lens brings an axis-parallel beam to F. Rays from a nearby object point need not arrive parallel, so their meeting point can be elsewhere.
Actual convergence or apparent convergence?
- Real image
- Actual refracted rays from an object point meet at the image point. A screen placed there can show a sharp image.
- Virtual image
- The emergent rays diverge, but their backward extensions meet at an apparent image point. A screen at that apparent position cannot collect actual converging rays to form the image.
- Upright or inverted
- Compare orientation with the object. For the upright arrow examples, an image arrow below the axis is inverted; one above it is upright.
- Magnified, same size or diminished
- Compare image height with object height. A greater, equal or smaller height gives the corresponding description.
You can see both real and virtual images when the appropriate light enters your eye. A screen test concerns actual convergence, not visibility.
Construct an image from two rays
- Draw the principal axis and the thin lens. Choose one length scale for both horizontal and vertical distances, and mark F on each side.
- Draw the upright object arrow at its stated position. Start both rays at its tip so they describe the same object point.
- Draw a ray parallel to the axis until it reaches the lens. After refraction it passes through the far principal focus.
- Draw a second ray from the object tip through the optical centre. It continues essentially straight in the thin-lens model.
- If actual emergent rays meet, draw the real image tip there. If they diverge, extend them backwards with dashed lines to find the virtual image tip.
- Complete the image arrow to the axis and read its position, height and orientation from the construction.
A ray directed through the near principal focus emerges parallel to the axis and can provide an additional check where that ray is used. Solid arrows show the direction light actually travels; dashed backward extensions do not show light travelling backwards.
Construct the examples below
Use f = 8 cm and a 2 cm tall object
First place the object 12 cm to the left. Its parallel ray reaches the lens 2 cm above the axis, then passes through the far focus 8 cm to the right. The ray through the optical centre meets it 24 cm to the right and 4 cm below the axis. That actual intersection locates the real image.
Now place the object only 4 cm to the left and apply the same two ray rules. The emergent rays diverge. Extend them backwards: their lines meet 8 cm to the left and 4 cm above the axis. This apparent intersection locates the virtual image. Do not bend a ray towards an imagined image before applying the ray rules.
In a paper drawing, a scale such as 1 cm representing 4 cm can be used in both directions. The screen figures below have their own labelled values; their physical size on your device is not a centimetre scale.
Read three completed diagrams
Each model uses a lens of focal length 8.0 cm and an upright object 2.0 cm tall. Identify which lines meet, then compare the image and object arrows.
Locate where rays, or their backward extensions, meet
Each completed diagram uses f = 8.0 cm and a 2.0 cm upright object. Horizontal and vertical distances have the same scale in all three panels. Use the supplied labels, not a ruler on your screen.
Blue and orange arrows represent the object and image. Green arrows show light travel. Dashed green lines are backward extensions.
A real, inverted, magnified image
The refracted rays meet at the image position. A screen placed there can receive a sharp image.
A real, inverted, diminished image
The refracted rays meet at the image position. A screen placed there can receive a sharp image.
A virtual, upright, magnified image
Only the backward extensions meet. The apparent image is on the object's side of the lens; the emerging light travels to the right.
- First diagram: real, inverted and magnified
- The actual rays meet 24 cm on the far side of the lens, 4 cm below the axis. The image is inverted and twice the 2 cm object height.
- Second diagram: real, inverted and diminished
- The rays meet 12 cm on the far side, 1 cm below the axis. The image is inverted and half the object height.
- Third diagram: virtual, upright and magnified
- Backward extensions meet 8 cm on the object's side, 4 cm above the axis. The actual emergent rays diverge. The image is upright and twice the object height.
These descriptions come from the completed ray paths and labelled sizes. The same converging lens can produce different image characteristics; it does not always magnify.
Connect the construction to object position
In the three examples, object distances from the lens are 12 cm, 24 cm and 4 cm respectively. Compare each with f = 8 cm and 2f = 16 cm. The first object lies between f and 2f, the second beyond 2f, and the third inside f.
| Object position | Image position | Image type |
|---|---|---|
| Beyond 2f | Between f and 2f on the other side | Real, inverted, diminished |
| At 2f | At 2f on the other side | Real, inverted, same size |
| Between f and 2f | Beyond 2f on the other side | Real, inverted, magnified |
| At f | No image on a screen at a finite distance | Emergent rays from one object point are parallel |
| Inside f | On the same side as the object | Virtual, upright, magnified |
At the ideal focal position, rays from one object point emerge parallel. Moving a screen farther away does not give a sharp finite-distance image in that ideal case. The image is not at F just because the object is at F.
Optional check A thin converging lens has focal length 8 cm. A 2 cm tall upright object is 4 cm to its left. A construction puts the backward intersection of emergent rays 8 cm to the left and 4 cm above the axis. How should the image be described?
Find an image and describe what you observe
For a real-image investigation, align an illuminated arrow, the lens and a screen along the principal axis. Move the screen until the image is sharp. Measure the image distance from the lens centre, then compare image height and orientation with the object. Use the same length units for a size comparison.
Move the object to another suitable position and refocus the screen. Keep the alignment and distinguish the lens-to-object distance from the lens-to-screen distance. A millimetre ruler can measure positions and heights, but a blurred edge limits how precisely the image height can be read.
For a supplied arrangement known to produce a virtual image, look through the lens at the object and describe the apparent image. It can be seen even though a screen at the apparent position does not show it. Its image position may be inferred from backward ray extensions.
A blurred screen is not proof of a virtual image. The screen may simply be in the wrong place or the apparatus misaligned. Use the ray behaviour and the stated setup as evidence.