ScienceAges 13-15

Converging lenses & focal length

Apply the thin lens equation 1/f = 1/u + 1/v to determine the focal length of a converging lens. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 13-15

Converging lenses & focal length

Take your time. Show your thinking.

1. An object is placed u = 140 cm in front of a converging lens, forming a sharp real image at v = 350 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 140 cm · Image v = 350 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 24 cm in front of a converging lens, forming a sharp real image at v = 48 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 24 cm · Image v = 48 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 420 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 180 cm · Image v = 420 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 30 cm in front of a converging lens, forming a sharp real image at v = 45 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 30 cm · Image v = 45 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 8 cm in front of a converging lens, forming a sharp real image at v = 8 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 8 cm · Image v = 8 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 28 cm in front of a converging lens, forming a sharp real image at v = 70 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 28 cm · Image v = 70 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 210 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 84 cm · Image v = 210 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 225 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 180 cm · Image v = 225 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 270 cm in front of a converging lens, forming a sharp real image at v = 630 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 270 cm · Image v = 630 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 385 cm in front of a converging lens, forming a sharp real image at v = 462 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 385 cm · Image v = 462 cm · Converging Lens: 1/f = 1/u + 1/v
11. An object is placed u = 132 cm in front of a converging lens, forming a sharp real image at v = 231 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 132 cm · Image v = 231 cm · Converging Lens: 1/f = 1/u + 1/v
12. An object is placed u = 5 cm in front of a converging lens, forming a sharp real image at v = 20 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 5 cm · Image v = 20 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 46 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Converging lenses & focal length

Answers and reasoning. Review before teaching.

1. An object is placed u = 140 cm in front of a converging lens, forming a sharp real image at v = 350 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
100 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (140 × 350) ÷ (140 + 350) = 49000 ÷ 490 = 100 cm.
2. An object is placed u = 24 cm in front of a converging lens, forming a sharp real image at v = 48 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
16 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (24 × 48) ÷ (24 + 48) = 1152 ÷ 72 = 16 cm.
3. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 420 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
126 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 420) ÷ (180 + 420) = 75600 ÷ 600 = 126 cm.
4. An object is placed u = 30 cm in front of a converging lens, forming a sharp real image at v = 45 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
18 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (30 × 45) ÷ (30 + 45) = 1350 ÷ 75 = 18 cm.
5. An object is placed u = 8 cm in front of a converging lens, forming a sharp real image at v = 8 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
4 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (8 × 8) ÷ (8 + 8) = 64 ÷ 16 = 4 cm.
6. An object is placed u = 28 cm in front of a converging lens, forming a sharp real image at v = 70 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
20 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (28 × 70) ÷ (28 + 70) = 1960 ÷ 98 = 20 cm.
7. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 210 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
60 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (84 × 210) ÷ (84 + 210) = 17640 ÷ 294 = 60 cm.
8. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 225 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
100 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 225) ÷ (180 + 225) = 40500 ÷ 405 = 100 cm.
9. An object is placed u = 270 cm in front of a converging lens, forming a sharp real image at v = 630 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
189 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (270 × 630) ÷ (270 + 630) = 170100 ÷ 900 = 189 cm.
10. An object is placed u = 385 cm in front of a converging lens, forming a sharp real image at v = 462 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
210 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (385 × 462) ÷ (385 + 462) = 177870 ÷ 847 = 210 cm.
11. An object is placed u = 132 cm in front of a converging lens, forming a sharp real image at v = 231 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
84 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (132 × 231) ÷ (132 + 231) = 30492 ÷ 363 = 84 cm.
12. An object is placed u = 5 cm in front of a converging lens, forming a sharp real image at v = 20 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
4 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (5 × 20) ÷ (5 + 20) = 100 ÷ 25 = 4 cm.

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Converging lenses & focal length

Take your time. Show your thinking.

1. An object is placed u = 140 cm in front of a converging lens, forming a sharp real image at v = 350 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 140 cm · Image v = 350 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 24 cm in front of a converging lens, forming a sharp real image at v = 48 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 24 cm · Image v = 48 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 420 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 180 cm · Image v = 420 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 30 cm in front of a converging lens, forming a sharp real image at v = 45 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 30 cm · Image v = 45 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 8 cm in front of a converging lens, forming a sharp real image at v = 8 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 8 cm · Image v = 8 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 28 cm in front of a converging lens, forming a sharp real image at v = 70 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 28 cm · Image v = 70 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 210 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 84 cm · Image v = 210 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 225 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 180 cm · Image v = 225 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 270 cm in front of a converging lens, forming a sharp real image at v = 630 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 270 cm · Image v = 630 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 385 cm in front of a converging lens, forming a sharp real image at v = 462 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 385 cm · Image v = 462 cm · Converging Lens: 1/f = 1/u + 1/v
11. An object is placed u = 132 cm in front of a converging lens, forming a sharp real image at v = 231 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 132 cm · Image v = 231 cm · Converging Lens: 1/f = 1/u + 1/v
12. An object is placed u = 5 cm in front of a converging lens, forming a sharp real image at v = 20 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 5 cm · Image v = 20 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Converging lenses & focal length

Answers and reasoning. Review before teaching.

1. An object is placed u = 140 cm in front of a converging lens, forming a sharp real image at v = 350 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
100 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (140 × 350) ÷ (140 + 350) = 49000 ÷ 490 = 100 cm.
2. An object is placed u = 24 cm in front of a converging lens, forming a sharp real image at v = 48 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
16 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (24 × 48) ÷ (24 + 48) = 1152 ÷ 72 = 16 cm.
3. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 420 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
126 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 420) ÷ (180 + 420) = 75600 ÷ 600 = 126 cm.
4. An object is placed u = 30 cm in front of a converging lens, forming a sharp real image at v = 45 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
18 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (30 × 45) ÷ (30 + 45) = 1350 ÷ 75 = 18 cm.
5. An object is placed u = 8 cm in front of a converging lens, forming a sharp real image at v = 8 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
4 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (8 × 8) ÷ (8 + 8) = 64 ÷ 16 = 4 cm.
6. An object is placed u = 28 cm in front of a converging lens, forming a sharp real image at v = 70 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
20 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (28 × 70) ÷ (28 + 70) = 1960 ÷ 98 = 20 cm.
7. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 210 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
60 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (84 × 210) ÷ (84 + 210) = 17640 ÷ 294 = 60 cm.
8. An object is placed u = 180 cm in front of a converging lens, forming a sharp real image at v = 225 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
100 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 225) ÷ (180 + 225) = 40500 ÷ 405 = 100 cm.
9. An object is placed u = 270 cm in front of a converging lens, forming a sharp real image at v = 630 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
189 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (270 × 630) ÷ (270 + 630) = 170100 ÷ 900 = 189 cm.
10. An object is placed u = 385 cm in front of a converging lens, forming a sharp real image at v = 462 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
210 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (385 × 462) ÷ (385 + 462) = 177870 ÷ 847 = 210 cm.
11. An object is placed u = 132 cm in front of a converging lens, forming a sharp real image at v = 231 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
84 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (132 × 231) ÷ (132 + 231) = 30492 ÷ 363 = 84 cm.
12. An object is placed u = 5 cm in front of a converging lens, forming a sharp real image at v = 20 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
4 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (5 × 20) ÷ (5 + 20) = 100 ÷ 25 = 4 cm.

12 questions · Seed 46 · Age guidance, not curriculum certification