Thin lenses and the lens maker's equation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Placing images with thin lenses

Science · Waves, Light & Sound · ages 19-20
Name ______________________   Date ____________

  1. An ideal thin lens's real image can be projected onto a screen placed at its image plane.

    Circle one:   True   False

  2. Which equation relates focal length f, object distance do and image distance di for an ideal thin lens?

    • 1/f = 1/do - 1/di
    • 1/f = 1/do + 1/di
    • 1/f = do + di + f

  3. In the ideal thin-lens model, what happens to a ray passing through the optical centre?

    • It turns toward the incoming-side focal point
    • It continues along the same straight line
    • It returns backward along its incoming ray path

  4. A real object has 0 < do < f for an ideal converging lens. Which image description is correct?

    • Real, inverted and greatly enlarged
    • Virtual, inverted and much reduced
    • Virtual, upright and enlarged

  5. An ideal thin lens has a real object at do = +40 cm and a real image at di = +20 cm. Give the signed magnification m.

    Answer: ______________

  6. A thin spherical lens in air has n = 1.5. Light travels left to right, with signed radii R1 = +24 cm and R2 = -24 cm. What is its focal length?

    • +24 cm
    • +12 cm
    • +48 cm

  7. An ideal converging lens has f = +10 cm and a real object at do = +30 cm. Using positive di for a real outgoing-side image, give the signed image distance in cm.

    Answer: ______________

  8. A single-lens camera model has fixed f > 0 and a real object beyond f. The object moves closer but stays beyond f. Sam claims that refocusing requires a smaller lens-to-sensor separation. Is this correct?

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Placing images with thin lenses W1-mt_FXOcC5mpIM-s1

  1. True · Actual outgoing rays from each object point meet at its corresponding image point.
  2. 1/f = 1/do + 1/di · The thin-lens equation adds the signed reciprocal object and image distances.
  3. It continues along the same straight line · The optical-centre ray is undeviated in the ideal thin-lens approximation.
  4. Virtual, upright and enlarged · di < 0 gives a virtual image. Also m = f/(f-do) > 1, so the image is upright and enlarged.
  5. -0.5 · m = -di/do = -20/40 = -0.5. The image is inverted and half-size.
  6. +24 cm · 1/f = (1.5-1)*(1/24-1/(-24)) = 1/24 per cm. Thus f = +24 cm.
  7. 15 · 1/di = 1/10 - 1/30 = 2/30 = 1/15 per cm. Thus di = +15 cm.
  8. False · The real image distance increases as the object approaches f from beyond it. The lens-to-sensor separation must increase.
Worksheet · LightMySky