How to use it
- Choose what to find: image distance, object distance or focal length.
- Enter the other two values in one length unit. Give a diverging lens or convex mirror a negative focal length.
- Optionally enter the object height.
- Read the result, the magnification, the image height and what kind of image forms.
Formulas
- Image distance: dᵢ = f × dₒ ÷ (dₒ − f).
- Object distance: dₒ = f × dᵢ ÷ (dᵢ − f).
- Focal length: f = dₒ × dᵢ ÷ (dₒ + dᵢ).
- Magnification: m = −dᵢ ÷ dₒ; image height = m × object height.
- Power: P = 1 ÷ f (f in metres), in dioptres.
Worked example
A converging lens with f = 10 cm and a 2 cm object 30 cm away: 1/dᵢ = 1/10 − 1/30, so dᵢ = 15 cm. The magnification is −15 ÷ 30 = −0.5: a real, inverted, reduced image 1 cm tall. The lens has a power of 10 D.
Move the object to 5 cm, inside the focal length: dᵢ = 10 × 5 ÷ (5 − 10) = −10 cm. The image is virtual, upright and twice as large, which is how a magnifying glass works.
Tips
- An object at the focal point sends parallel rays: the image is at infinity and there is no finite answer.
- An object at 2f gives a real, inverted image of the same size, also at 2f.
- A diverging lens always gives a virtual, upright, reduced image of a real object.