Light · Model
Lenses and images
A hole in a box makes a picture, and it makes a bad bargain doing it: sharp or bright, never both. A lens is the piece of glass that refuses the bargain.
Start here
A box with a pin-prick in it shows you the world upside down.
Take a shoebox, make one clean pin-prick in one end and stretch greaseproof paper across the other. Point the pin-prick at a bright window. A picture of the window appears on the paper, in colour, and it is upside down and the wrong way round.
There is no lens, no glass and nothing electrical in the box. Why is the picture inverted?
Straight lines, and nothing else. To get through the hole at all, light from the top of the window has to be travelling downwards — so it carries on downwards and lands low on the screen. Light from the bottom is travelling upwards and lands high. The two cross at the hole, and everything in between crosses with them.
Light travels in straight lines, and every point on a bright object throws light out in every direction. The hole is what makes the picture: out of the whole spray of light leaving the top of the window, only the one ray aimed at the hole gets through, and it carries on in a straight line to a single place on the screen. Because it was heading downwards to reach the hole, it keeps heading downwards afterwards, and lands near the bottom. Light from the bottom of the window does the reverse. The rays cross at the hole, and the picture arrives inverted.
A pinhole camera has one problem, and it is a trap you cannot get out of. A smaller hole picks out one ray per point and gives a sharp picture, but lets very little light through, so the picture is dim. A bigger hole lets more light through and is brighter, but now a whole small bundle of rays gets through from each point and lands as a patch rather than a point, so the picture blurs.
A convex lens — one that bulges outwards — breaks the trap. It refracts every ray in the bundle by just the right amount to bring them all back together at one place, so a wide opening can be used and the picture is bright and sharp. A pinhole selects one ray and throws the rest away; a lens collects them and puts them back together. That is what focusing means.
At the bench · a pinhole camera and a lit object 300 mm tall
Three things to change. Two of them fight each other.
Change a control to begin
A lit object 300 mm tall in front of a box with one hole in it and a screen at the back. Set how far away the object is, how long the box is, and how wide the hole is.
Commit first. The box is made twice as long and nothing else is touched. What happens to the picture on the screen?
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How wide the hole is
Picture height on the screen
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How blurred each point is
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How much light gets in
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against the narrowest hole
Which way up
Upside down, and left for right
at every setting
The figure
What a convex lens does that a hole cannot
Parallel rays, brought to one point
Every ray is refracted twice, going in and coming out, and the shape of the glass is chosen so that all of them arrive at the same place. The wider the lens, the more light it gathers — and the picture stays sharp.
An object, and its picture
All the light leaving one point of the object and passing anywhere through the lens is brought back to one point on the screen. The rays still cross, so the picture is still upside down — a lens fixes the brightness and the sharpness, not the inversion.
A pinhole throws away almost all the light in order to be sharp. A lens keeps it and puts it back in the right place. That is the whole reason eyes and cameras have lenses in them and not pin-pricks.
Key fact
Light travels in straight lines, so the rays from the top and bottom of an object cross at a pinhole and the picture on the screen is upside down. A narrow hole gives a sharp but dim picture and a wide one a bright but blurred picture. A convex lens refracts all the rays from one point of the object back to one point on the screen, so a wide opening can be both bright and sharp — but the rays still cross, so the picture is still inverted.
Think again
“The pinhole flips the picture over, so a lens must flip it back.”
Nothing does any flipping. The rays from the top of the object are travelling downwards when they reach the hole, so they carry on downwards afterwards and land low on the screen; the rays from the bottom are travelling upwards and land high. The inversion is just where straight lines go. A lens changes how much light gets through and where it lands, and does nothing about that crossing — which is why the picture inside a camera and the picture on the back of your eye are both upside down.
“A bigger hole makes a bigger picture.”
It makes a brighter and blurrier one, and leaves the size exactly where it was. Only two things set the size: how far away the object is, and how long the box is. The bench above will show you — change the hole from the narrowest to the widest and the picture height reading does not move at all, while the blur reading grows tenfold. Size and sharpness are set by different controls, and the commonest way to get this wrong is to assume that the one you can see changing is the one doing the work.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Apply the rule
A pinhole camera gives a picture 40 mm tall. The box is then made twice as long, with the object left exactly where it was. What is the new picture height?
Rung 2 · The one that catches people
A pinhole picture is too dim to see clearly, so a student widens the hole. Which statement is right?
Rung 3 · Explain
Explain why the picture in a pinhole camera is upside down, using the idea that light travels in straight lines.
Rung 4 · Take it somewhere new
Eyes and cameras could have been built with a pinhole instead of a lens, and none of them are. Explain what a convex lens gives them that a pinhole cannot, and name one thing that stays the same either way.
Key note
Light travels in straight lines, so rays from the top and bottom of an object cross at a pinhole and the picture on the screen is inverted. Its size is set by how far away the object is and how long the box is, and by nothing else. A narrow hole is sharp and dim; a wide one is bright and blurred. A convex lens refracts all the rays leaving one point of the object back to a single point on the screen, so a wide opening gives a picture that is bright and sharp at once — and still upside down.
Going further
Where the picture lands depends on how far away the object is, which is a problem for anything that has to look at near and far things with the same lens. A camera solves it by moving the lens backwards and forwards until the picture falls exactly on the sensor. Your eye cannot do that, because the retina is a fixed distance behind the lens, so it changes the lens instead: a ring of muscle squeezes the lens fatter to look at something close and lets it go thinner for something far away. The same job, two completely different engineering answers, and the fact that reading for hours is tiring is a muscle in your eye complaining.
Before this lesson
Connects to
At GCSE this becomes
- Ray diagrams for converging and diverging lenses, focal length and magnification, real and virtual images, and correcting short and long sight.
Where to next
Ask Mr Badmus AI
Got a pinhole camera to work out the picture size for?
Never look directly at the Sun — not with your eyes, not through a lens, not through a pinhole camera. A lens gathers sunlight to a point hot enough to scorch paper, and it will do the same to the back of your eye. The damage is painless while it happens and it does not heal.
The bench is a teaching model. The two arrow heights are drawn to one scale, so the ratio between the picture and the object is exactly right; distances along the axis are compressed to fit the width, and the hole is placed so that the drawn rays remain straight. The blur is drawn as the thickness of the picture arrow, to the same scale as the heights, with a minimum thickness so that the sharpest setting still draws. Brightness is quoted as a comparison with the narrowest hole and follows the area of the hole, which ignores losses in the box and the spreading of the picture over a larger screen. The object is treated as evenly lit and 300 mm tall throughout, and the screen as a flat surface at the back of the box.
Lesson content © MrBadmusAI.