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 = 216 cm in front of a converging lens, forming a sharp real image at v = 360 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 = 360 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 50 cm in front of a converging lens, forming a sharp real image at v = 200 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 50 cm · Image v = 200 cm · Converging Lens: 1/f = 1/u + 1/v
3. 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
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 = 360 cm in front of a converging lens, forming a sharp real image at v = 450 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 360 cm · Image v = 450 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 40 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 = 40 cm · Image v = 60 cm · Converging Lens: 1/f = 1/u + 1/v
7. 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
8. An object is placed u = 420 cm in front of a converging lens, forming a sharp real image at v = 588 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 420 cm · Image v = 588 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 144 cm in front of a converging lens, forming a sharp real image at v = 504 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 144 cm · Image v = 504 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 40 cm in front of a converging lens, forming a sharp real image at v = 160 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 40 cm · Image v = 160 cm · Converging Lens: 1/f = 1/u + 1/v
11. 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
12. An object is placed u = 20 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 = 20 cm · Image v = 60 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 43 · 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 = 216 cm in front of a converging lens, forming a sharp real image at v = 360 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
135 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (216 × 360) ÷ (216 + 360) = 77760 ÷ 576 = 135 cm.
2. An object is placed u = 50 cm in front of a converging lens, forming a sharp real image at v = 200 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
40 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (50 × 200) ÷ (50 + 200) = 10000 ÷ 250 = 40 cm.
3. 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.
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 = 360 cm in front of a converging lens, forming a sharp real image at v = 450 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
200 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (360 × 450) ÷ (360 + 450) = 162000 ÷ 810 = 200 cm.
6. An object is placed u = 40 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.
24 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (40 × 60) ÷ (40 + 60) = 2400 ÷ 100 = 24 cm.
7. 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.
8. An object is placed u = 420 cm in front of a converging lens, forming a sharp real image at v = 588 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
245 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (420 × 588) ÷ (420 + 588) = 246960 ÷ 1008 = 245 cm.
9. An object is placed u = 144 cm in front of a converging lens, forming a sharp real image at v = 504 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
112 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (144 × 504) ÷ (144 + 504) = 72576 ÷ 648 = 112 cm.
10. An object is placed u = 40 cm in front of a converging lens, forming a sharp real image at v = 160 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
32 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (40 × 160) ÷ (40 + 160) = 6400 ÷ 200 = 32 cm.
11. 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.
12. An object is placed u = 20 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.
15 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (20 × 60) ÷ (20 + 60) = 1200 ÷ 80 = 15 cm.

12 questions · Seed 43 · 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 = 216 cm in front of a converging lens, forming a sharp real image at v = 360 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 = 360 cm · Converging Lens: 1/f = 1/u + 1/v
2. An object is placed u = 50 cm in front of a converging lens, forming a sharp real image at v = 200 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 50 cm · Image v = 200 cm · Converging Lens: 1/f = 1/u + 1/v
3. 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
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 = 360 cm in front of a converging lens, forming a sharp real image at v = 450 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 360 cm · Image v = 450 cm · Converging Lens: 1/f = 1/u + 1/v
6. An object is placed u = 40 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 = 40 cm · Image v = 60 cm · Converging Lens: 1/f = 1/u + 1/v
7. 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
8. An object is placed u = 420 cm in front of a converging lens, forming a sharp real image at v = 588 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 420 cm · Image v = 588 cm · Converging Lens: 1/f = 1/u + 1/v
9. An object is placed u = 144 cm in front of a converging lens, forming a sharp real image at v = 504 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 144 cm · Image v = 504 cm · Converging Lens: 1/f = 1/u + 1/v
10. An object is placed u = 40 cm in front of a converging lens, forming a sharp real image at v = 160 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
Object u = 40 cm · Image v = 160 cm · Converging Lens: 1/f = 1/u + 1/v
11. 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
12. An object is placed u = 20 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 = 20 cm · Image v = 60 cm · Converging Lens: 1/f = 1/u + 1/v

12 questions · Seed 43 · 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 = 216 cm in front of a converging lens, forming a sharp real image at v = 360 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
135 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (216 × 360) ÷ (216 + 360) = 77760 ÷ 576 = 135 cm.
2. An object is placed u = 50 cm in front of a converging lens, forming a sharp real image at v = 200 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
40 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (50 × 200) ÷ (50 + 200) = 10000 ÷ 250 = 40 cm.
3. 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.
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 = 360 cm in front of a converging lens, forming a sharp real image at v = 450 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
200 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (360 × 450) ÷ (360 + 450) = 162000 ÷ 810 = 200 cm.
6. An object is placed u = 40 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.
24 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (40 × 60) ÷ (40 + 60) = 2400 ÷ 100 = 24 cm.
7. 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.
8. An object is placed u = 420 cm in front of a converging lens, forming a sharp real image at v = 588 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
245 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (420 × 588) ÷ (420 + 588) = 246960 ÷ 1008 = 245 cm.
9. An object is placed u = 144 cm in front of a converging lens, forming a sharp real image at v = 504 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
112 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (144 × 504) ÷ (144 + 504) = 72576 ÷ 648 = 112 cm.
10. An object is placed u = 40 cm in front of a converging lens, forming a sharp real image at v = 160 cm on the other side. Using 1/f = 1/u + 1/v, calculate the focal length f of the lens.
32 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (40 × 160) ÷ (40 + 160) = 6400 ÷ 200 = 32 cm.
11. 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.
12. An object is placed u = 20 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.
15 cm
Using 1/f = 1/u + 1/v gives f = (u × v) ÷ (u + v) = (20 × 60) ÷ (20 + 60) = 1200 ÷ 80 = 15 cm.

12 questions · Seed 43 · Age guidance, not curriculum certification