Thin Lens Equation Calculator
Calculate object distance, image distance, focal length, and magnification for thin lenses
Calculate Thin Lens Properties
Distance from object to lens center
Lens focal length (+ for converging, - for diverging)
Calculation Results
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
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
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