Thin Lens Equation Calculator

Calculate object distance, image distance, focal length, and magnification for thin lenses

Calculate Thin Lens Properties

cm

Distance from object to lens center

cm

Lens focal length (+ for converging, - for diverging)

Calculation Results

Enter the required values to calculate lens properties

Make sure all required fields are filled and the object is not at the focal point

Example Calculations

Converging Lens Example

Given: Object distance = 30 cm, Focal length = +20 cm

Calculation: 1/y = 1/20 - 1/30 = (3-2)/60 = 1/60

Result: Image distance = 60 cm (real, magnified image)

Magnification: M = 60/30 = 2× (inverted, twice the size)

Diverging Lens Example

Given: Object distance = 20 cm, Focal length = -15 cm

Calculation: 1/y = 1/(-15) - 1/20 = (-4-3)/60 = -7/60

Result: Image distance = -8.57 cm (virtual, diminished image)

Magnification: M = 8.57/20 = 0.43× (upright, smaller)

Key Formulas

Thin Lens Equation
1/f = 1/x + 1/y
Magnification
M = |y|/x
Lens Power
P = 1/f (in diopters)

Sign Conventions

+

Focal length: Converging lens

Focal length: Diverging lens

+

Image distance: Real image

Image distance: Virtual image

Lens Types

Converging (Convex)

f > 0, focuses light rays

Diverging (Concave)

f < 0, spreads light rays

Applications

👓

Eyeglasses and contact lenses

📷

Camera and projector lenses

🔬

Microscopes and telescopes

💡

Magnifying glasses

⚗️

Scientific instruments

Understanding the Thin Lens Equation

The Lens Equation

The thin lens equation relates the object distance (x), image distance (y), and focal length (f) of a thin lens. This fundamental relationship allows us to predict where an image will form and its characteristics.

Key Concepts

  • Focal Length: Distance from lens center to focal point
  • Object Distance: Distance from object to lens center
  • Image Distance: Distance from lens center to image

Image Characteristics

1/f = 1/x + 1/y
M = |y|/x

Real vs Virtual Images

Real Image (y > 0): Can be projected on a screen, formed on opposite side of lens

Virtual Image (y > 0): Cannot be projected, appears on same side as object

Converging Lens Cases

Object beyond 2F

Real, inverted, diminished image

Object at 2F

Real, inverted, same size image

Object between F and 2F

Real, inverted, magnified image

Object inside F

Virtual, upright, magnified image

Practical Applications

Corrective Lenses

Eyeglasses use lens power (diopters) to correct vision

Optical Instruments

Microscopes and telescopes use lens combinations

Photography

Camera lenses focus light to form real images