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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Age band:Ages 13-15 Ages 16-18

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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 = 16 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 = 16 cm · Image v = 48 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 2 cm in front of a converging lens, forming a sharp real image at v = 2 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 2 cm · Image v = 2 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 324 cm in front of a converging lens, forming a sharp real image at v = 405 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 324 cm · Image v = 405 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 6 cm in front of a converging lens, forming a sharp real image at v = 12 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 6 cm · Image v = 12 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 10 cm in front of a converging lens, forming a sharp real image at v = 40 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 10 cm · Image v = 40 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 112 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 = 112 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 60 cm · Image v = 140 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 42 cm in front of a converging lens, forming a sharp real image at v = 56 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 42 cm · Image v = 56 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 210 cm in front of a converging lens, forming a sharp real image at v = 280 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 210 cm · Image v = 280 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 = 35 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 35 cm · Image v = 140 cm · Converging Lens: 1/f = 1/u + 1/v
12. An object is placed u = 108 cm in front of a converging lens, forming a sharp real image at v = 378 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 108 cm · Image v = 378 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 48 · 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 = 16 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.
12 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (16 × 48) ÷ (16 + 48) = 768 ÷ 64 = 12 cm.
2. An object is placed u = 2 cm in front of a converging lens, forming a sharp real image at v = 2 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
1 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (2 × 2) ÷ (2 + 2) = 4 ÷ 4 = 1 cm.
3. An object is placed u = 324 cm in front of a converging lens, forming a sharp real image at v = 405 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
180 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (324 × 405) ÷ (324 + 405) = 131220 ÷ 729 = 180 cm.
4. An object is placed u = 6 cm in front of a converging lens, forming a sharp real image at v = 12 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) = (6 × 12) ÷ (6 + 12) = 72 ÷ 18 = 4 cm.
5. An object is placed u = 10 cm in front of a converging lens, forming a sharp real image at v = 40 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
8 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (10 × 40) ÷ (10 + 40) = 400 ÷ 50 = 8 cm.
6. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 112 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
48 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (84 × 112) ÷ (84 + 112) = 9408 ÷ 196 = 48 cm.
7. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
42 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (60 × 140) ÷ (60 + 140) = 8400 ÷ 200 = 42 cm.
8. An object is placed u = 42 cm in front of a converging lens, forming a sharp real image at v = 56 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
24 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (42 × 56) ÷ (42 + 56) = 2352 ÷ 98 = 24 cm.
9. An object is placed u = 210 cm in front of a converging lens, forming a sharp real image at v = 280 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
120 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (210 × 280) ÷ (210 + 280) = 58800 ÷ 490 = 120 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 = 35 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
28 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (35 × 140) ÷ (35 + 140) = 4900 ÷ 175 = 28 cm.
12. An object is placed u = 108 cm in front of a converging lens, forming a sharp real image at v = 378 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) = (108 × 378) ÷ (108 + 378) = 40824 ÷ 486 = 84 cm.

12 questions · Seed 48 · 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 = 16 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 = 16 cm · Image v = 48 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 2 cm in front of a converging lens, forming a sharp real image at v = 2 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 2 cm · Image v = 2 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 324 cm in front of a converging lens, forming a sharp real image at v = 405 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 324 cm · Image v = 405 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 6 cm in front of a converging lens, forming a sharp real image at v = 12 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 6 cm · Image v = 12 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 10 cm in front of a converging lens, forming a sharp real image at v = 40 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 10 cm · Image v = 40 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 112 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 = 112 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 60 cm · Image v = 140 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 42 cm in front of a converging lens, forming a sharp real image at v = 56 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 42 cm · Image v = 56 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 210 cm in front of a converging lens, forming a sharp real image at v = 280 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 210 cm · Image v = 280 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 = 35 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 35 cm · Image v = 140 cm · Converging Lens: 1/f = 1/u + 1/v
12. An object is placed u = 108 cm in front of a converging lens, forming a sharp real image at v = 378 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 108 cm · Image v = 378 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 48 · 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 = 16 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.
12 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (16 × 48) ÷ (16 + 48) = 768 ÷ 64 = 12 cm.
2. An object is placed u = 2 cm in front of a converging lens, forming a sharp real image at v = 2 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
1 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (2 × 2) ÷ (2 + 2) = 4 ÷ 4 = 1 cm.
3. An object is placed u = 324 cm in front of a converging lens, forming a sharp real image at v = 405 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
180 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (324 × 405) ÷ (324 + 405) = 131220 ÷ 729 = 180 cm.
4. An object is placed u = 6 cm in front of a converging lens, forming a sharp real image at v = 12 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) = (6 × 12) ÷ (6 + 12) = 72 ÷ 18 = 4 cm.
5. An object is placed u = 10 cm in front of a converging lens, forming a sharp real image at v = 40 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
8 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (10 × 40) ÷ (10 + 40) = 400 ÷ 50 = 8 cm.
6. An object is placed u = 84 cm in front of a converging lens, forming a sharp real image at v = 112 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
48 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (84 × 112) ÷ (84 + 112) = 9408 ÷ 196 = 48 cm.
7. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
42 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (60 × 140) ÷ (60 + 140) = 8400 ÷ 200 = 42 cm.
8. An object is placed u = 42 cm in front of a converging lens, forming a sharp real image at v = 56 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
24 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (42 × 56) ÷ (42 + 56) = 2352 ÷ 98 = 24 cm.
9. An object is placed u = 210 cm in front of a converging lens, forming a sharp real image at v = 280 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
120 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (210 × 280) ÷ (210 + 280) = 58800 ÷ 490 = 120 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 = 35 cm in front of a converging lens, forming a sharp real image at v = 140 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
28 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (35 × 140) ÷ (35 + 140) = 4900 ÷ 175 = 28 cm.
12. An object is placed u = 108 cm in front of a converging lens, forming a sharp real image at v = 378 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) = (108 × 378) ÷ (108 + 378) = 40824 ÷ 486 = 84 cm.

12 questions · Seed 48 · Age guidance, not curriculum certification