Lens & Mirror Calculator

Lenses and mirrors form images by refracting or reflecting light. The lens/mirror equation and magnification formula allow you to calculate image and object properties for a wide range of optical systems.

Key Formulas:

• 1/f = 1/d₀ + 1/dᵢ - Lens/Mirror equation
• m = -dᵢ/d₀ - Magnification
• hᵢ = m × h₀ - Image height

Sign Conventions:

• Focal length (f): Positive for converging (convex lens, concave mirror), negative for diverging (concave lens, convex mirror)
• Object distance (d₀): Positive if object is on the incoming side of the lens/mirror
• Image distance (dᵢ): Positive if image is on the outgoing side (real), negative if virtual
• Heights: Positive above axis, negative below

Applications:

• Eyeglasses and contact lenses
• Microscopes and telescopes
• Cameras and projectors
• Mirrors in optical instruments