Thin Lens Formula
Relate object distance, image distance, and focal length for thin lenses.
Core formula for lens and camera design.
The Formula
1/f = 1/dₒ + 1/dᵢ
The thin lens formula connects the focal length of a lens to the distances of the object and its image. It works for both converging (convex) and diverging (concave) lenses.
Variables
| Symbol | Meaning |
|---|---|
| f | Focal length of the lens (positive for convex, negative for concave) |
| dₒ | Object distance — distance from the object to the lens |
| dᵢ | Image distance — distance from the lens to the image |
Example 1
An object is 30 cm from a lens with focal length 10 cm. Where is the image?
1/10 = 1/30 + 1/dᵢ
1/dᵢ = 1/10 - 1/30 = 3/30 - 1/30 = 2/30
dᵢ = 15 cm (real image, on the opposite side of the lens)
Example 2
An object is 20 cm from a diverging lens with f = -15 cm. Where is the image?
1/(-15) = 1/20 + 1/dᵢ
1/dᵢ = -1/15 - 1/20 = -4/60 - 3/60 = -7/60
dᵢ = -8.57 cm (virtual image, same side as the object)
When to Use It
Use the thin lens formula when:
- Designing cameras, telescopes, or microscopes
- Finding where an image forms for a given lens and object position
- Calculating the focal length needed for a specific magnification
- Understanding how eyeglasses correct vision