The Camera
Simple Explanation
A camera uses a converging lens to focus light from an object onto a light-sensitive sensor (or film), forming a real, inverted image — exactly as predicted by the thin lens equation, 1/f=1/v+1/u.
Why Do We Need It?
Understanding how a camera's lens forms an image is the foundation for every other optical instrument in this chapter — the eye, microscope, and telescope all use the same lens equation in different arrangements.
See It
An object on the left with two light rays passing through a converging lens, meeting again on the right to form a smaller, inverted image on the sensor
Formula
The Thin Lens Equation
1/f = 1/v + 1/u
A camera's converging lens forms a sharp, focused image on the sensor (or film) exactly where the lens equation predicts, given the lens's focal length and the object's distance.
- f
- — focal length of the lens, in metres (m)
- v
- — image distance — from the lens to the focused image, in metres (m)
- u
- — object distance — from the lens to the object being photographed, in metres (m)
When to use it: Whenever the distance a camera lens must be from its sensor to form a sharp image of an object at a given distance needs to be found.
Worked Example
Find where a camera lens focuses an image
A camera lens has a focal length of 0.05 m (50 mm). It photographs an object 3 m away. Find the image distance behind the lens.
Why Does This Work?
Every ray leaving a point on the object and passing through a converging lens is bent so that all such rays reconverge at a single point — the image point — and the lens equation is exactly the mathematical statement of where that convergence happens, derived from the geometry of light bending at the lens.
Real-Life Example
Autofocus adjusting a camera lens
A camera's autofocus system physically moves the lens slightly closer to or farther from the sensor as the photographer changes what they are photographing.
This is the camera solving the lens equation in real time — moving the lens to the correct v for whatever object distance u it detects, keeping the image sharply focused.
Practice
A camera lens (f=0.04 m) photographs an object 2 m away. Find the image distance, rounded to 4 decimal places.
MediumCommon mistake
Forgetting that the image formed on a camera sensor is INVERTED — the lens equation gives the correct distance, but the image is upside down (which the camera's software or the eye/brain corrects for afterward).
Quick Review
- 1/f = 1/v + 1/u — the thin lens equation.
- Forms a real, inverted image on the sensor.
- The foundation for every optical instrument in this chapter.