Lens Calculator

Calculate focal length, image distance, magnification, and other optical properties

Lens Parameters

Enter lens properties and object position

cm
cm
cm
Image Distance (v)
60 cm
Distance from lens to image
Magnification (m)
-2.00
Image size relative to object
Image Height (h')
-10 cm
Height of the image
Image Type
Real, Inverted
Focal Length Calculation

Calculate focal length from object and image distances

cm
cm
Focal Length (f)
-60 cm
Lens focal length
Magnification (m)
-2.00
Image size relative to object
Object
Image
Lens
F₁
F₂

Understanding Lenses

Lenses are optical devices that refract light to form images. They are essential components in cameras, telescopes, microscopes, and eyeglasses.

1

Convex Lenses: Converging lenses that focus parallel rays to a focal point

Can produce real or virtual images depending on object position

2

Concave Lenses: Diverging lenses that spread parallel rays apart

Always produce virtual, upright, and reduced images

3

Focal Length: Distance from lens to focal point

Determines lens power (P = 1/f in diopters)

4

Magnification: Ratio of image height to object height

m = -v/u = hᵢ/hₒ

Lens Formulas
1/f = 1/v - 1/u
m = v/u = h'/h
Where:
f = Focal length
u = Object distance
v = Image distance
m = Magnification
h = Object height
h' = Image height

Key Concepts

Focal Length
f
Determines lens power
Object Distance
u
Always negative
Image Distance
v
Positive for real images
Magnification
m
|m|>1: enlarged, |m|<1: reduced

Lens Types

Convex Lenses

Converging lenses used in magnifying glasses, cameras, and telescopes

Concave Lenses

Diverging lenses used in eyeglasses for myopia correction

Compound Lenses

Combinations of lenses to correct aberrations in optical systems

Lens Applications
Application Lens Type Focal Length Typical Use
Human eye Convex ~17mm Focusing light on retina
Camera lens Convex 18-300mm Photography
Magnifying glass Convex 5-20cm Magnifying small objects
Eyeglasses (myopia) Concave -25 to -200cm Correcting nearsightedness
Telescope objective Convex 500-2000mm Astronomy
Microscope objective Convex 2-40mm High magnification

Convex Lenses:

  • Thicker in the center than at the edges
  • Converge parallel light rays to a focal point
  • Can produce real or virtual images
  • Used in magnifying glasses, cameras, telescopes

Concave Lenses:

  • Thinner in the center than at the edges
  • Diverge parallel light rays
  • Always produce virtual, upright, and reduced images
  • Used in eyeglasses for nearsightedness correction

For convex lenses:

Object Position Image Type Image Orientation Size
Beyond 2F Real Inverted Reduced
At 2F Real Inverted Same size
Between F and 2F Real Inverted Enlarged
At F No image - -
Inside F Virtual Upright Enlarged

For concave lenses:

  • Always produces virtual, upright, and reduced images
  • Image is always between the lens and the focal point

Lens Power: Measure of a lens's ability to converge or diverge light

Formula: P = 1/f

Where:

  • P = Lens power in diopters (D)
  • f = Focal length in meters

Key points:

  • Convex lenses have positive power
  • Concave lenses have negative power
  • Higher power = stronger lens
  • Example: f=0.5m → P=2D
  • Eyeglass prescriptions use diopters

Lens aberrations are imperfections in image formation:

Aberration Description Correction
Spherical Aberration Rays at edge focus differently than center Aspheric lenses, aperture stop
Chromatic Aberration Different colors focus at different points Achromatic doublet lenses
Coma Off-axis points appear comet-shaped Aspheric surfaces, aperture stop
Astigmatism Different focus for tangential and sagittal rays Complex lens designs
Distortion Straight lines appear curved Symmetric lens arrangements