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 = 72 cm in front of a converging lens, forming a sharp real image at v = 252 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 72 cm · Image v = 252 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 45 cm in front of a converging lens, forming a sharp real image at v = 180 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 45 cm · Image v = 180 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 70 cm in front of a converging lens, forming a sharp real image at v = 105 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 70 cm · Image v = 105 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 = 60 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 = 60 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 100 cm in front of a converging lens, forming a sharp real image at v = 150 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 100 cm · Image v = 150 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 180 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 = 180 cm · Image v = 630 cm · Converging Lens: 1/f = 1/u + 1/v
7. 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
8. An object is placed u = 308 cm in front of a converging lens, forming a sharp real image at v = 539 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 308 cm · Image v = 539 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 480 cm in front of a converging lens, forming a sharp real image at v = 672 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 480 cm · Image v = 672 cm · Converging Lens: 1/f = 1/u + 1/v
10. 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
11. 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
12. An object is placed u = 18 cm in front of a converging lens, forming a sharp real image at v = 36 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 18 cm · Image v = 36 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 44 · 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 = 72 cm in front of a converging lens, forming a sharp real image at v = 252 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
56 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (72 × 252) ÷ (72 + 252) = 18144 ÷ 324 = 56 cm.
2. An object is placed u = 45 cm in front of a converging lens, forming a sharp real image at v = 180 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
36 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (45 × 180) ÷ (45 + 180) = 8100 ÷ 225 = 36 cm.
3. An object is placed u = 70 cm in front of a converging lens, forming a sharp real image at v = 105 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) = (70 × 105) ÷ (70 + 105) = 7350 ÷ 175 = 42 cm.
4. An object is placed u = 30 cm in front of a converging lens, forming a sharp real image at v = 60 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) = (30 × 60) ÷ (30 + 60) = 1800 ÷ 90 = 20 cm.
5. An object is placed u = 100 cm in front of a converging lens, forming a sharp real image at v = 150 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) = (100 × 150) ÷ (100 + 150) = 15000 ÷ 250 = 60 cm.
6. An object is placed u = 180 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.
140 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 630) ÷ (180 + 630) = 113400 ÷ 810 = 140 cm.
7. 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.
8. An object is placed u = 308 cm in front of a converging lens, forming a sharp real image at v = 539 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
196 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (308 × 539) ÷ (308 + 539) = 166012 ÷ 847 = 196 cm.
9. An object is placed u = 480 cm in front of a converging lens, forming a sharp real image at v = 672 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
280 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (480 × 672) ÷ (480 + 672) = 322560 ÷ 1152 = 280 cm.
10. 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.
11. 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.
12. An object is placed u = 18 cm in front of a converging lens, forming a sharp real image at v = 36 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) = (18 × 36) ÷ (18 + 36) = 648 ÷ 54 = 12 cm.

12 questions · Seed 44 · 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 = 72 cm in front of a converging lens, forming a sharp real image at v = 252 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 72 cm · Image v = 252 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 45 cm in front of a converging lens, forming a sharp real image at v = 180 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 45 cm · Image v = 180 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 70 cm in front of a converging lens, forming a sharp real image at v = 105 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 70 cm · Image v = 105 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 = 60 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 = 60 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 100 cm in front of a converging lens, forming a sharp real image at v = 150 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 100 cm · Image v = 150 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 180 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 = 180 cm · Image v = 630 cm · Converging Lens: 1/f = 1/u + 1/v
7. 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
8. An object is placed u = 308 cm in front of a converging lens, forming a sharp real image at v = 539 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 308 cm · Image v = 539 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 480 cm in front of a converging lens, forming a sharp real image at v = 672 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 480 cm · Image v = 672 cm · Converging Lens: 1/f = 1/u + 1/v
10. 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
11. 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
12. An object is placed u = 18 cm in front of a converging lens, forming a sharp real image at v = 36 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 18 cm · Image v = 36 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 44 · 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 = 72 cm in front of a converging lens, forming a sharp real image at v = 252 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
56 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (72 × 252) ÷ (72 + 252) = 18144 ÷ 324 = 56 cm.
2. An object is placed u = 45 cm in front of a converging lens, forming a sharp real image at v = 180 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
36 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (45 × 180) ÷ (45 + 180) = 8100 ÷ 225 = 36 cm.
3. An object is placed u = 70 cm in front of a converging lens, forming a sharp real image at v = 105 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) = (70 × 105) ÷ (70 + 105) = 7350 ÷ 175 = 42 cm.
4. An object is placed u = 30 cm in front of a converging lens, forming a sharp real image at v = 60 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) = (30 × 60) ÷ (30 + 60) = 1800 ÷ 90 = 20 cm.
5. An object is placed u = 100 cm in front of a converging lens, forming a sharp real image at v = 150 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) = (100 × 150) ÷ (100 + 150) = 15000 ÷ 250 = 60 cm.
6. An object is placed u = 180 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.
140 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 630) ÷ (180 + 630) = 113400 ÷ 810 = 140 cm.
7. 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.
8. An object is placed u = 308 cm in front of a converging lens, forming a sharp real image at v = 539 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
196 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (308 × 539) ÷ (308 + 539) = 166012 ÷ 847 = 196 cm.
9. An object is placed u = 480 cm in front of a converging lens, forming a sharp real image at v = 672 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
280 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (480 × 672) ÷ (480 + 672) = 322560 ÷ 1152 = 280 cm.
10. 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.
11. 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.
12. An object is placed u = 18 cm in front of a converging lens, forming a sharp real image at v = 36 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) = (18 × 36) ÷ (18 + 36) = 648 ÷ 54 = 12 cm.

12 questions · Seed 44 · Age guidance, not curriculum certification