Answer key: Converging Lens Worksheet
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Goal: Use the thin-lens equation 1/f = 1/dₒ + 1/dᵢ to predict where a converging lens forms an image, and whether it is real or virtual, inverted or upright, larger or smaller.
Completed results table
| Setting | Image distance | Magnification | Image type | Orientation |
|---|---|---|---|---|
| Object at 25 cm (Real image) | 16.67 cm | -0.67 | Real | Inverted |
| Object at 20 cm (Same size) | 20 cm | -1 | Real | Inverted |
| Object at 10 cm (At the focus) | No finite image | Undefined | Parallel rays | — |
| Object at 6 cm (Magnifier) | -15 cm | 2.5 | Virtual | Upright |
| Object at 15 cm | 30 cm | -2 | Real | Inverted |
| Object at 40 cm | 13.33 cm | -0.33 | Real | Inverted |
Answers
Use 1/f = 1/dₒ + 1/dᵢ to calculate the image distance for the object at 25 cm. Does it match the lab?
1/dᵢ = 1/10 − 1/25 = 0.06 cm⁻¹, so dᵢ = 16.67 cm, matching the lab. The image is real and inverted.
When is the image the same size as the object? Explain with the magnification M = −dᵢ/dₒ.
When the object is at 20 cm, twice the focal length. The image also forms 20 cm from the lens, so M = −20 ÷ 20 = −1: the same size, but inverted.
As you moved the object from 40 cm to 15 cm, what happened to the image?
It moved away from the lens and grew: from 13.33 cm with M = −0.33 (smaller than the object) to 30 cm with M = −2 (twice as large). Moving an object toward the focal point pushes the real image farther out and enlarges it.
What happened when the object was exactly at the focal point (10 cm)?
No image formed. The rays leave the lens parallel to each other, so they never meet: 1/dᵢ = 1/10 − 1/10 = 0, which means the image is infinitely far away.
With the object at 6 cm, inside the focal length, the image distance is negative. What does that mean, and where is this used?
A negative image distance (−15 cm) means a virtual image on the same side as the object: the rays spread out after the lens and only appear to come from that point. The image is upright and 2.5 times larger, which is exactly what a magnifying glass shows you.
Challenge: predict where the image forms for an object 60 cm from the same lens, then check it.
1/dᵢ = 1/10 − 1/60, so dᵢ = 12 cm and M = −0.2: a small, inverted, real image just past the focal point, like a camera photographing a distant object.