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Optics

Lenses, Mirrors & Images

Where the picture actually is when there is no screen to catch it, and what covering half the lens does to it.

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Lenses, Mirrors & Images

Where the picture actually is when there is no screen to catch it, and what covering half the lens does to it.

35 min4 checkpoints9 simulation tasks

Introduction

A magnifying glass can throw a sunlit window onto a sheet of paper, upside down. So where was that picture before the paper arrived?

Predict

A lens projects a sharp image of a lit arrow onto a screen. You slide a card over the top half of the lens. What happens to the image?

One point, one image point

Try it

Run it, then cover more and more of the lens until it gathers only about 5% of the light. Watch the image.

GoalThe lens gathers only about 5% of the light.

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The lens does not make the image, the way a printer makes a page. It only bends every ray that reaches it. The image is where the rays from one point of the object meet again, out in the air.

Three rays are enough

Rays from one point of the object all meet at its image point. Three are easy to draw:

  1. In parallel to the axis, out through the far focus.
  2. Through the centre, straight on.
  3. In through the near focus, out parallel.

Any two cross there.

Try it

Move the object so the image forms 20 cm away.

GoalThe image 20 cm behind the lens.

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Predict

Use the equation. Set the object distance that puts the image 30 cm behind this lens, with f=10f = 10 cm, then run.

GoalThe image 30 cm behind the lens.

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Does the image need a screen?

Try it

Run it. The picture on the screen is a blur. Slide the screen until the picture is sharp.

GoalA sharp picture on the screen.

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Predict

The lens projects a sharp image onto a screen 15 cm behind it. You take the screen away. What is now where the screen used to be?

Try it

Now the screen sits at 20 cm, and the picture is blurred by ±1.67 cm. Without moving the screen, cover the lens until the blur is down to ±0.50 cm.

GoalThe blur on the screen down to ±0.50 cm.

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Images you cannot catch

Bring the object closer than the focal length and the rays leaving the lens spread apart. They never cross, so there is nowhere to put a screen.

Try it

This lens has f=10f = 10 cm. Slide the object in until the image is upright and two and a half times as big.

GoalAn upright image, 2.5 times as big.

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The dashed backward extensions meet at a point, bigger and the right way up: a virtual image. The light reaching your eye behaves as if it came from there. It did not.

Practice

A magnifying glass held 6 cm from a stamp (f = 10 cm) shows a large, upright stamp. Where is that enlarged stamp, and what is there?

Try it

A diverging lens, f=−10f = -10 cm. Slide the object until its image is half the object's height.

GoalAn image half the object's height.

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Mirrors keep the same equation

A concave mirror obeys the same equation as a converging lens. Only the outgoing side changes: light comes back, so a real image forms in front of the mirror, and a virtual one behind the glass.

Try it

Here f=10f = 10 cm. Move the object until the image is real, inverted and the same size.

GoalA real, inverted image the same size as the object.

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Practice

A concave mirror has f = 10 cm. You put an object 6 cm in front of it. What do you get?

Try it

Make a shaving mirror: move the object until its image is upright and twice its size.

GoalAn upright image twice the object's size.

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What comes next

Every ray in this lesson travelled in a straight line between surfaces. Next, light that will not: two slits, and a pattern that rays cannot explain.

Ideas this lesson took on

Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.

  • “Covering half the lens removes half the image”
  • “Without a screen there is no image”
  • “A virtual image is imaginary, so it is not anywhere”
  • “A concave mirror can only make real images”

Finished with this lesson?

Progress is stored on this device only. There is no account and nothing is sent anywhere.

Research behind this lesson

  • Goldberg & McDermott 1986: Individual demonstration interviews with a real plane mirror: students who could state the law of reflection could not use it to say what an observer standing in a particular place would actually see, and did not connect the lines of a ray diagram to the light that has to arrive at an eye.
  • Goldberg & McDermott 1987: In interviews built round a lit bulb, a converging lens and a screen, only about a third of students recognised that even a small part of a lens still forms the whole image; the most popular answer to covering half the lens was "half a lens, half an image", and having just completed the optics course made no difference to the result.
  • McDermott & Shaffer 2002: A research-validated elicit–confront–resolve sequence: surface the intuitive belief explicitly, put it in direct conflict with evidence, then help rebuild. Skipping the confrontation leaves the original belief intact alongside the new formalism.