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 = 21 cm in front of a converging lens, forming a sharp real image at v = 42 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 21 cm · Image v = 42 cm · Converging Lens: 1/f = 1/u + 1/v
2. 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
3. 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
4. An object is placed u = 180 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 = 180 cm · Image v = 252 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 240 cm in front of a converging lens, forming a sharp real image at v = 336 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 240 cm · Image v = 336 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 216 cm in front of a converging lens, forming a sharp real image at v = 270 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 216 cm · Image v = 270 cm · Converging Lens: 1/f = 1/u + 1/v
7. 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
8. An object is placed u = 18 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 = 18 cm · Image v = 18 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 330 cm in front of a converging lens, forming a sharp real image at v = 396 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 330 cm · Image v = 396 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 72 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 = 72 cm · Image v = 120 cm · Converging Lens: 1/f = 1/u + 1/v
11. An object is placed u = 495 cm in front of a converging lens, forming a sharp real image at v = 594 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 495 cm · Image v = 594 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 42 · 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 = 21 cm in front of a converging lens, forming a sharp real image at v = 42 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
14 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (21 × 42) ÷ (21 + 42) = 882 ÷ 63 = 14 cm.
2. 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.
3. 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.
4. An object is placed u = 180 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.
105 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 252) ÷ (180 + 252) = 45360 ÷ 432 = 105 cm.
5. An object is placed u = 240 cm in front of a converging lens, forming a sharp real image at v = 336 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) = (240 × 336) ÷ (240 + 336) = 80640 ÷ 576 = 140 cm.
6. An object is placed u = 216 cm in front of a converging lens, forming a sharp real image at v = 270 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) = (216 × 270) ÷ (216 + 270) = 58320 ÷ 486 = 120 cm.
7. 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.
8. An object is placed u = 18 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.
9 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (18 × 18) ÷ (18 + 18) = 324 ÷ 36 = 9 cm.
9. An object is placed u = 330 cm in front of a converging lens, forming a sharp real image at v = 396 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) = (330 × 396) ÷ (330 + 396) = 130680 ÷ 726 = 180 cm.
10. An object is placed u = 72 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.
45 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (72 × 120) ÷ (72 + 120) = 8640 ÷ 192 = 45 cm.
11. An object is placed u = 495 cm in front of a converging lens, forming a sharp real image at v = 594 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
270 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (495 × 594) ÷ (495 + 594) = 294030 ÷ 1089 = 270 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 42 · 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 = 21 cm in front of a converging lens, forming a sharp real image at v = 42 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 21 cm · Image v = 42 cm · Converging Lens: 1/f = 1/u + 1/v
2. 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
3. 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
4. An object is placed u = 180 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 = 180 cm · Image v = 252 cm · Converging Lens: 1/f = 1/u + 1/v
5. An object is placed u = 240 cm in front of a converging lens, forming a sharp real image at v = 336 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 240 cm · Image v = 336 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 216 cm in front of a converging lens, forming a sharp real image at v = 270 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 216 cm · Image v = 270 cm · Converging Lens: 1/f = 1/u + 1/v
7. 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
8. An object is placed u = 18 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 = 18 cm · Image v = 18 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 330 cm in front of a converging lens, forming a sharp real image at v = 396 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 330 cm · Image v = 396 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 72 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 = 72 cm · Image v = 120 cm · Converging Lens: 1/f = 1/u + 1/v
11. An object is placed u = 495 cm in front of a converging lens, forming a sharp real image at v = 594 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 495 cm · Image v = 594 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 42 · 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 = 21 cm in front of a converging lens, forming a sharp real image at v = 42 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
14 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (21 × 42) ÷ (21 + 42) = 882 ÷ 63 = 14 cm.
2. 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.
3. 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.
4. An object is placed u = 180 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.
105 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (180 × 252) ÷ (180 + 252) = 45360 ÷ 432 = 105 cm.
5. An object is placed u = 240 cm in front of a converging lens, forming a sharp real image at v = 336 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) = (240 × 336) ÷ (240 + 336) = 80640 ÷ 576 = 140 cm.
6. An object is placed u = 216 cm in front of a converging lens, forming a sharp real image at v = 270 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) = (216 × 270) ÷ (216 + 270) = 58320 ÷ 486 = 120 cm.
7. 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.
8. An object is placed u = 18 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.
9 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (18 × 18) ÷ (18 + 18) = 324 ÷ 36 = 9 cm.
9. An object is placed u = 330 cm in front of a converging lens, forming a sharp real image at v = 396 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) = (330 × 396) ÷ (330 + 396) = 130680 ÷ 726 = 180 cm.
10. An object is placed u = 72 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.
45 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (72 × 120) ÷ (72 + 120) = 8640 ÷ 192 = 45 cm.
11. An object is placed u = 495 cm in front of a converging lens, forming a sharp real image at v = 594 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
270 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (495 × 594) ÷ (495 + 594) = 294030 ÷ 1089 = 270 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 42 · Age guidance, not curriculum certification