Waves Equations Worksheet
Practice the wave equations with 10 problems covering wave speed, frequency, period, and wavelength. Includes full worked answers.
View worksheet →Lenses and Mirrors Equations Worksheet
Practice with 10 problems on the thin lens equation, mirror equation, magnification, and image formation. Full worked solutions included.
Equations you will need
| 1/f = 1/u + 1/v | Thin lens / mirror equation |
| M = -v/u | Magnification (linear) |
| M = h_i / h_o | Magnification from image and object height |
| P = 1/f | Lens power |
Symbol key
| Symbol | Quantity | Unit |
|---|---|---|
| f | focal length | m |
| u | object distance | m |
| v | image distance | m |
| M | magnification | dimensionless |
| h_o | object height | m |
| h_i | image height | m |
| P | power | D (dioptres) |
Practice problems
Attempt each problem on paper first, then click Show answer to check your working.
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Object 30 cm from a converging lens with f = 10 cm. Find image distance.
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1/10 = 1/30 + 1/v → v = 15 cm -
Same setup: find magnification.
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M = -15/30 = -0.5 (inverted, reduced) -
A 5 cm tall object 20 cm from a lens, f = 15 cm. Find image height.
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1/15 = 1/20 + 1/v → v = 60 cm; M = -3; h_i = -15 cm (inverted) -
Find focal length of a lens with power +2.5 D.
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f = 1/P = 0.4 m = 40 cm -
Object 12 cm from a concave mirror with f = 20 cm. Find v.
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1/20 = 1/12 + 1/v → v = -30 cm (virtual, behind mirror) -
A converging lens (f = 8 cm) forms an image at 24 cm. Find the object distance.
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1/8 = 1/u + 1/24 → u = 12 cm -
A diverging lens with f = -10 cm: object at 15 cm. Find image position.
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-1/10 = 1/15 + 1/v → v = -6 cm (virtual) -
Object at f (focal point) of a converging lens. Where is image?
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Image at infinity (parallel rays) -
Magnifying glass: object 4 cm from f = 8 cm lens. Find magnification.
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1/8 = 1/4 + 1/v → v = -8 cm; M = -(-8)/4 = 2 (upright, virtual, enlarged) -
A camera lens with f = 50 mm photographs an object 2 m away. Find image distance.
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1/0.05 = 1/2 + 1/v → v = 0.0513 m = 51.3 mm
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About this worksheet
This lenses and mirrors equations worksheet covers the essential equations for waves & optics at the GCSE / A-Level / AP Physics 2 level. Every problem has been written to mirror the style and difficulty of real exam questions, with full algebraic working shown in the solutions.
If you find these problems too straightforward, try the more advanced worksheets in the same topic listed above. If they feel too difficult, start by reviewing the equation definitions in the box at the top of this page and then return to question 1.