Predicting Image Location
The Mirror/Lens Equation is a simple yet powerful formula that allows you to predict exactly where an image will form when an object is placed in front of a mirror or a lens. It is used to design telescopes, microscopes, and cameras.
It relates three key distances:
- Focal Length ($f$): The distance from the center of the lens/mirror to the point where parallel light rays converge.
- Object Distance ($d_o$): The distance from the object (the thing you are looking at) to the lens.
- Image Distance ($d_i$): The distance from the lens to where the image actually appears (like where you would place a sensor or film).
Sign Conventions
This is the trickiest part of the equation:
- Converging (Convex Lens / Concave Mirror): $f$ is positive.
- Diverging (Concave Lens / Convex Mirror): $f$ is negative.
- Real Image: $d_i$ is positive (it forms on the opposite side of the lens or in front of a mirror).
- Virtual Image: $d_i$ is negative (it appears 'inside' the lens or behind a mirror).
The Formula
Where:
f=
Focal Length=
Distance to Object=
Distance to ImageExample Calculation
You place a candle $30 , \text{cm}$ ($0.3 , \text{m}$) in front of a converging lens with a focal length of $10 , \text{cm}$ ($0.1 , \text{m}$).
- Calculate 1/f and 1/do: $1 / 0.1 = 10$ and $1 / 0.3 \approx 3.33$.
- Subtract: $10 - 3.33 = 6.67$.
- Invert for di: $1 / 6.67 = 0.15 , \text{m}$.
A real, inverted image of the candle will form $15 , \text{cm} behind the lens.