CSEC PHYSICS · SECTION C · LESSON C9

Magnification, the Lens Formula and Finding the Focal Length

Calculating magnification from image and object sizes or distances, applying 1/f = 1/u + 1/v with a sign convention, and methods to find the focal length of a converging lens.

Waves and OpticsC 5.4C 5.5≈ 40 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON C9 · EXPLAINER

Magnification, the Lens Formula and Finding the Focal Length

A scale diagram is a good guide, but a formula gives the exact answer. With the lens formula you can predict where the screen must go.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Magnification

m = h_i/h_o = v/u; no unit.

Lens formula

1/f = 1/u + 1/v.

Real-is-positive

Real: positive distances; virtual image: v negative.

Convex lens

f positive; concave lens: f negative.

Real image

v positive; inverted.

Virtual image

v negative; upright; magnifying glass when u < f.

Distant object method

Image of a far object forms at the focal plane: v ≈ f.

u–v method

f = uv ÷ (u + v).

EXAM TIPS & COMMON MISTAKES

  • Keep units consistent (all cm or all m).
  • Find v by adding fractions carefully: 1/v = 1/f − 1/u.
  • A negative v means a virtual image on the same side as the object.
  • Magnification: use the positive value for the size, and say whether the image is inverted or upright.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Physics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

Syllabus C 5.4

1. The magnification produced by a lens is

Answer: A. m = h_i ÷ h_o.
Syllabus C 5.4

2. An object 4.0 cm tall forms an image 12.0 cm tall. The magnification is

Answer: B. 12 ÷ 4 = 3.0.
Syllabus C 5.4

3. A convex lens has f = 10 cm. An object at u = 30 cm gives an image at v =

Answer: B. 1/v = 1/10 − 1/30 = 1/15.
Syllabus C 5.4

4. In the previous question the magnification is

Answer: A. m = v ÷ u = 15 ÷ 30 = 0.5.
Syllabus C 5.4

5. A negative value of v from the lens formula means the image is

Answer: C. Virtual image, same side as the object.
Syllabus C 5.5

6. A convex lens forms a real image at v = 24 cm of an object at u = 24 cm. The focal length is

Answer: D. 1/f = 1/24 + 1/24 = 1/12.
Syllabus C 5.5

7. To estimate the focal length of a converging lens quickly, a student focuses the image of a distant window on a screen. The measured distance is approximately

Answer: A. Light from a distant object is nearly parallel.
Syllabus C 5.5

8. Using the u–v method with u = 20 cm and v = 20 cm gives a focal length of

Answer: B. f = uv ÷ (u + v) = 400 ÷ 40.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (15 marks in total). Show all your working — method marks count. Your answers are saved on this device.

Paper 2 style · The lens formula

Question 1 [15 marks]

A convex lens of focal length 10.0 cm forms an image of a 6.0 cm tall object placed 25.0 cm from the lens.

(a) (a) State the lens formula and define each symbol. [3]

MARK SCHEME — (a) (max 3)

(b) (b) Calculate the image distance. [3]

MARK SCHEME — (b) (max 3)

(c) (c) Calculate the magnification. [2]

MARK SCHEME — (c) (max 2)

(d) (d) Calculate the height of the image. [2]

MARK SCHEME — (d) (max 2)

(e) (e) State two characteristics of the image. [2]

MARK SCHEME — (e) (max 2)

(f) (f) Describe one method to find the focal length of the lens in the laboratory. [3]

MARK SCHEME — (f) (max 3)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.