ScienceAges 16-18

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 16-18

Converging lenses & focal length

Take your time. Show your thinking.

1. An object is placed u = 14 cm in front of a converging lens, forming a sharp real image at v = 35 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 14 cm · Image v = 35 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 90 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 = 90 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 30 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 = 30 cm · Image v = 70 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 84 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 = 84 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 24 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 = 24 cm · Image v = 40 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 36 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 = 36 cm · Image v = 45 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 264 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 220 cm · Image v = 264 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 300 cm in front of a converging lens, forming a sharp real image at v = 700 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 300 cm · Image v = 700 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 147 cm in front of a converging lens, forming a sharp real image at v = 196 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 147 cm · Image v = 196 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 396 cm in front of a converging lens, forming a sharp real image at v = 693 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 396 cm · Image v = 693 cm · Converging Lens: 1/f = 1/u + 1/v
11. An object is placed u = 80 cm in front of a converging lens, forming a sharp real image at v = 120 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 80 cm · Image v = 120 cm · Converging Lens: 1/f = 1/u + 1/v
12. An object is placed u = 9 cm in front of a converging lens, forming a sharp real image at v = 18 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 9 cm · Image v = 18 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 45 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Converging lenses & focal length

Answers and reasoning. Review before teaching.

1. An object is placed u = 14 cm in front of a converging lens, forming a sharp real image at v = 35 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
10 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (14 × 35) ÷ (14 + 35) = 490 ÷ 49 = 10 cm.
2. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 90 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) = (60 × 90) ÷ (60 + 90) = 5400 ÷ 150 = 36 cm.
3. An object is placed u = 30 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.
21 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (30 × 70) ÷ (30 + 70) = 2100 ÷ 100 = 21 cm.
4. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 84 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
35 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (60 × 84) ÷ (60 + 84) = 5040 ÷ 144 = 35 cm.
5. An object is placed u = 24 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.
15 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (24 × 40) ÷ (24 + 40) = 960 ÷ 64 = 15 cm.
6. An object is placed u = 36 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.
20 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (36 × 45) ÷ (36 + 45) = 1620 ÷ 81 = 20 cm.
7. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 264 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) = (220 × 264) ÷ (220 + 264) = 58080 ÷ 484 = 120 cm.
8. An object is placed u = 300 cm in front of a converging lens, forming a sharp real image at v = 700 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) = (300 × 700) ÷ (300 + 700) = 210000 ÷ 1000 = 210 cm.
9. An object is placed u = 147 cm in front of a converging lens, forming a sharp real image at v = 196 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) = (147 × 196) ÷ (147 + 196) = 28812 ÷ 343 = 84 cm.
10. An object is placed u = 396 cm in front of a converging lens, forming a sharp real image at v = 693 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
252 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (396 × 693) ÷ (396 + 693) = 274428 ÷ 1089 = 252 cm.
11. An object is placed u = 80 cm in front of a converging lens, forming a sharp real image at v = 120 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) = (80 × 120) ÷ (80 + 120) = 9600 ÷ 200 = 48 cm.
12. An object is placed u = 9 cm in front of a converging lens, forming a sharp real image at v = 18 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
6 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (9 × 18) ÷ (9 + 18) = 162 ÷ 27 = 6 cm.

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Converging lenses & focal length

Take your time. Show your thinking.

1. An object is placed u = 14 cm in front of a converging lens, forming a sharp real image at v = 35 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 14 cm · Image v = 35 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 90 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 = 90 cm · Converging Lens: 1/f = 1/u + 1/v
3. An object is placed u = 30 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 = 30 cm · Image v = 70 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 84 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 = 84 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 24 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 = 24 cm · Image v = 40 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 36 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 = 36 cm · Image v = 45 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 264 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 220 cm · Image v = 264 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 300 cm in front of a converging lens, forming a sharp real image at v = 700 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 300 cm · Image v = 700 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 147 cm in front of a converging lens, forming a sharp real image at v = 196 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 147 cm · Image v = 196 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 396 cm in front of a converging lens, forming a sharp real image at v = 693 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 396 cm · Image v = 693 cm · Converging Lens: 1/f = 1/u + 1/v
11. An object is placed u = 80 cm in front of a converging lens, forming a sharp real image at v = 120 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 80 cm · Image v = 120 cm · Converging Lens: 1/f = 1/u + 1/v
12. An object is placed u = 9 cm in front of a converging lens, forming a sharp real image at v = 18 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 9 cm · Image v = 18 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Converging lenses & focal length

Answers and reasoning. Review before teaching.

1. An object is placed u = 14 cm in front of a converging lens, forming a sharp real image at v = 35 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
10 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (14 × 35) ÷ (14 + 35) = 490 ÷ 49 = 10 cm.
2. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 90 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) = (60 × 90) ÷ (60 + 90) = 5400 ÷ 150 = 36 cm.
3. An object is placed u = 30 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.
21 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (30 × 70) ÷ (30 + 70) = 2100 ÷ 100 = 21 cm.
4. An object is placed u = 60 cm in front of a converging lens, forming a sharp real image at v = 84 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
35 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (60 × 84) ÷ (60 + 84) = 5040 ÷ 144 = 35 cm.
5. An object is placed u = 24 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.
15 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (24 × 40) ÷ (24 + 40) = 960 ÷ 64 = 15 cm.
6. An object is placed u = 36 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.
20 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (36 × 45) ÷ (36 + 45) = 1620 ÷ 81 = 20 cm.
7. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 264 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) = (220 × 264) ÷ (220 + 264) = 58080 ÷ 484 = 120 cm.
8. An object is placed u = 300 cm in front of a converging lens, forming a sharp real image at v = 700 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) = (300 × 700) ÷ (300 + 700) = 210000 ÷ 1000 = 210 cm.
9. An object is placed u = 147 cm in front of a converging lens, forming a sharp real image at v = 196 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) = (147 × 196) ÷ (147 + 196) = 28812 ÷ 343 = 84 cm.
10. An object is placed u = 396 cm in front of a converging lens, forming a sharp real image at v = 693 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
252 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (396 × 693) ÷ (396 + 693) = 274428 ÷ 1089 = 252 cm.
11. An object is placed u = 80 cm in front of a converging lens, forming a sharp real image at v = 120 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) = (80 × 120) ÷ (80 + 120) = 9600 ÷ 200 = 48 cm.
12. An object is placed u = 9 cm in front of a converging lens, forming a sharp real image at v = 18 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
6 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (9 × 18) ÷ (9 + 18) = 162 ÷ 27 = 6 cm.

12 questions · Seed 45 · Age guidance, not curriculum certification