Thin Lens Equation
Relates focal length to object and image distances.
Formula
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How it works
The thin lens equation connects where an object is placed, where its image forms, and the lens’s focal length. It comes from the geometry of rays passing through an ideal thin lens: one ray through the center is treated as nearly undeviated, and another ray parallel to the axis refracts through the focal point, so the similar triangles in the ray diagram give the relationship. It is most accurate for thin lenses and paraxial rays, meaning rays close to the optical axis and small angles.
When to use it
Use this formula whenever you need to find an unknown object distance, image distance, or focal length for a converging or diverging lens in ray-diagram problems. It is common in lab optics, camera and projector modeling, and basic vision/lens calculations.
Worked example, step by step
A converging lens has focal length f = 15 cm. An object is placed 30 cm from the lens. Find the image distance. 1/15 = 1/30 + 1/d_i 1/d_i = 1/15 - 1/30 1/d_i = 2/30 - 1/30 = 1/30 d_i = 30 cm Final answer: the image forms 30 cm from the lens.
Common mistakes to avoid
- Mixing up object distance and image distance, especially when rearranging the equation
- Forgetting that distances may be negative in sign-convention-based problems
- Using the thin lens equation for thick lenses or very wide-angle rays where the approximation breaks down
Did You Know?
The thin-lens equation lets opticians grind the exact lens needed to bring your world back into focus.
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