What it shows
The size, position and nature of the image in a concave mirror change as the object moves from far away to inside the focal length. The mirror formula and magnification can be checked with real readings.
The science
A concave mirror of focal length f and a real object at distance u form an image at v given by 1/u + 1/v = 1/f (real distances positive). The magnification is m = v / u. For u > 2f the image is real, inverted and smaller; at u = 2f it is the same size; between f and 2f it is real, inverted and larger; at u < f the image is virtual, upright and larger, and cannot be caught on a screen. The focal length is half the radius of curvature.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A concave shaving or make-up mirror (about 20 to 30 cm focal length)
- A torch or a candle-substitute LED lamp with a cross-wire stencil
- A white card screen
- A metre rule or tape on a table
- Clay or clothes pegs for holders
- Graph paper
Safety
For this project: Do not let the mirror focus the Sun on skin, paper or cloth; an adult must supervise outdoor tests of the focal length.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Find a rough f by focusing a distant window or the Sun’s image on a card; note the distance from the mirror to the sharp spot.
Stand the mirror upright on the rule and put the lit stencil at 3f, a bit to one side of the axis so the screen does not block it.
Move the card in front of the mirror until the inverted image of the cross is sharp and note v.
Move the object to 2.5f, 2f, 1.5f and 1.2f in turn and find v each time.
Measure the image and object sizes and calculate magnification m = h_i / h_o and v / u for each position.
Place the object at less than f, look into the mirror and describe the image you see (upright, bigger, behind the mirror).
Compute f from each pair of u and v using the mirror formula and compare with the rough f.
Summarise all six cases in a table with position, size, nature and orientation of the image.
What you should see
The six cases match the ray diagrams: small real image beyond 2f, equal at 2f, large real image between f and 2f, and a virtual upright one inside f. Values of f from the formula agree with the quick estimate.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the relation between f and the radius of curvature?
f = R / 2.
2Why can a virtual image not be caught on a screen?
Light only appears to come from it; the rays do not actually meet there.
3Where is the object for the largest real image?
Just beyond the focus, where the image forms far away and is very big.
4Where are concave mirrors used?
In shaving mirrors, torch and headlight reflectors and dentists’ mirrors.
Take it further
Use a spoon-sized convex mirror and show that it always gives a small, upright, virtual image.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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