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 = 162 cm in front of a converging lens, forming a sharp real image at v = 567 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 162 cm · Image v = 567 cm · Converging Lens: 1/f = 1/u + 1/v
2. 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
3. An object is placed u = 275 cm in front of a converging lens, forming a sharp real image at v = 330 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 275 cm · Image v = 330 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 36 cm in front of a converging lens, forming a sharp real image at v = 108 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 = 108 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 20 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 = 20 cm · Image v = 20 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 90 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 = 90 cm · Image v = 210 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 16 cm in front of a converging lens, forming a sharp real image at v = 16 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 = 16 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 385 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 = 385 cm · Converging Lens: 1/f = 1/u + 1/v
9. 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
10. An object is placed u = 48 cm in front of a converging lens, forming a sharp real image at v = 80 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 48 cm · Image v = 80 cm · Converging Lens: 1/f = 1/u + 1/v
11. 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
12. An object is placed u = 105 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 = 105 cm · Image v = 140 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 47 · 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 = 162 cm in front of a converging lens, forming a sharp real image at v = 567 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) = (162 × 567) ÷ (162 + 567) = 91854 ÷ 729 = 126 cm.
2. 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.
3. An object is placed u = 275 cm in front of a converging lens, forming a sharp real image at v = 330 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
150 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (275 × 330) ÷ (275 + 330) = 90750 ÷ 605 = 150 cm.
4. An object is placed u = 36 cm in front of a converging lens, forming a sharp real image at v = 108 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
27 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (36 × 108) ÷ (36 + 108) = 3888 ÷ 144 = 27 cm.
5. An object is placed u = 20 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.
10 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (20 × 20) ÷ (20 + 20) = 400 ÷ 40 = 10 cm.
6. An object is placed u = 90 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.
63 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (90 × 210) ÷ (90 + 210) = 18900 ÷ 300 = 63 cm.
7. An object is placed u = 16 cm in front of a converging lens, forming a sharp real image at v = 16 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) = (16 × 16) ÷ (16 + 16) = 256 ÷ 32 = 8 cm.
8. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 385 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) = (220 × 385) ÷ (220 + 385) = 84700 ÷ 605 = 140 cm.
9. 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.
10. An object is placed u = 48 cm in front of a converging lens, forming a sharp real image at v = 80 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
30 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (48 × 80) ÷ (48 + 80) = 3840 ÷ 128 = 30 cm.
11. 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.
12. An object is placed u = 105 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.
60 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (105 × 140) ÷ (105 + 140) = 14700 ÷ 245 = 60 cm.

12 questions · Seed 47 · 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 = 162 cm in front of a converging lens, forming a sharp real image at v = 567 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 162 cm · Image v = 567 cm · Converging Lens: 1/f = 1/u + 1/v
2. 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
3. An object is placed u = 275 cm in front of a converging lens, forming a sharp real image at v = 330 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 275 cm · Image v = 330 cm · Converging Lens: 1/f = 1/u + 1/v
4. An object is placed u = 36 cm in front of a converging lens, forming a sharp real image at v = 108 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 = 108 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 20 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 = 20 cm · Image v = 20 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 90 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 = 90 cm · Image v = 210 cm · Converging Lens: 1/f = 1/u + 1/v
7. An object is placed u = 16 cm in front of a converging lens, forming a sharp real image at v = 16 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 = 16 cm · Converging Lens: 1/f = 1/u + 1/v
8. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 385 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 = 385 cm · Converging Lens: 1/f = 1/u + 1/v
9. 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
10. An object is placed u = 48 cm in front of a converging lens, forming a sharp real image at v = 80 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 48 cm · Image v = 80 cm · Converging Lens: 1/f = 1/u + 1/v
11. 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
12. An object is placed u = 105 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 = 105 cm · Image v = 140 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 47 · 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 = 162 cm in front of a converging lens, forming a sharp real image at v = 567 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) = (162 × 567) ÷ (162 + 567) = 91854 ÷ 729 = 126 cm.
2. 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.
3. An object is placed u = 275 cm in front of a converging lens, forming a sharp real image at v = 330 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
150 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (275 × 330) ÷ (275 + 330) = 90750 ÷ 605 = 150 cm.
4. An object is placed u = 36 cm in front of a converging lens, forming a sharp real image at v = 108 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
27 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (36 × 108) ÷ (36 + 108) = 3888 ÷ 144 = 27 cm.
5. An object is placed u = 20 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.
10 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (20 × 20) ÷ (20 + 20) = 400 ÷ 40 = 10 cm.
6. An object is placed u = 90 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.
63 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (90 × 210) ÷ (90 + 210) = 18900 ÷ 300 = 63 cm.
7. An object is placed u = 16 cm in front of a converging lens, forming a sharp real image at v = 16 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) = (16 × 16) ÷ (16 + 16) = 256 ÷ 32 = 8 cm.
8. An object is placed u = 220 cm in front of a converging lens, forming a sharp real image at v = 385 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) = (220 × 385) ÷ (220 + 385) = 84700 ÷ 605 = 140 cm.
9. 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.
10. An object is placed u = 48 cm in front of a converging lens, forming a sharp real image at v = 80 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
30 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (48 × 80) ÷ (48 + 80) = 3840 ÷ 128 = 30 cm.
11. 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.
12. An object is placed u = 105 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.
60 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (105 × 140) ÷ (105 + 140) = 14700 ÷ 245 = 60 cm.

12 questions · Seed 47 · Age guidance, not curriculum certification