Waves & Optics
Lens & Mirror Calculator
Solve 1/v + 1/u = 1/f for image distance, object distance or focal length. Shows magnification and image type.
Result
1/v + 1/u = 1/f
Magnification (m)
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Step-by-Step Solution
The Lens & Mirror Equation
The thin lens equation (also called the mirror equation) relates the object distance (u), image distance (v) and focal length (f) of a thin lens or spherical mirror. It allows prediction of where an image will form and whether it will be real or virtual, upright or inverted, magnified or diminished.
1/v + 1/u = 1/f | m = −v/u
v = image distance (m) | u = object distance (m) | f = focal length (m) | m = magnification
💡 Sign convention: distances measured from the optical centre. Real images (v > 0) are formed on the far side; virtual images (v < 0) are on the same side as the object. A negative magnification means the image is inverted.
Real-World Applications
Human Eye
The eye's lens focuses images on the retina by changing focal length. Glasses correct for defects in this process.
Cameras
Camera lenses form real, inverted images on the sensor. The focal length determines zoom and field of view.
Telescopes
Objective lens forms a real image; eyepiece magnifies it. Focal lengths determine total magnification.
Microscopes
Two converging lenses — objective and eyepiece — provide extreme magnification of small samples.
Frequently Asked Questions
What is the sign convention for the lens equation?
Using the real-is-positive convention: object distance u is positive (real object). Image distance v is positive for real images (on far side of lens) and negative for virtual images (same side as object). Focal length f is positive for converging lenses/concave mirrors and negative for diverging lenses/convex mirrors.
When is the image virtual?
When the object is inside the focal length of a converging lens (u < f), the image is virtual (v < 0), upright and magnified. This is how a magnifying glass works. Virtual images cannot be projected onto a screen.
What is magnification?
Linear magnification m = −v/u = image height/object height. |m| > 1 means the image is larger than the object. m < 0 means the image is inverted. m = +0.5 means the image is half the size and upright.