Thin Lens Studio

Solve the ideal thin-lens equation. Enter any two independent parameters to solve the rest, or enter more to analyze design residuals.

Lens Parameters

Enter numerical values. Leave fields blank to solve for them.

Paraxial Ray Diagram

FF'ObjectImage
■ Central Ray■ Parallel Ray■ Focal Ray

Calculation Results

Focal Length (f)100 mm
Optical Power10 D
Object Distance (d_o)200 mm
Image Distance (d_i)200 mm
Magnification (m)-1
Image Height (h_i)-10 mm

Image Characteristics

Type: REAL IMAGE
Orientation: INVERTED
Scale: SAME-SIZE

Thin-Lens Imaging Theory

Thin Lens Equation

1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Relates focal length, object distance, and image distance. Uses the sign conventions defined below.

Transverse Magnification

m=−dido=hihom = -\frac{d_i}{d_o} = \frac{h_i}{h_o}

Computes the ratio of image height to object height. A negative magnification indicates an inverted image.

Optical Power

P=1fmeters=1000fmmP = \frac{1}{f_{\mathrm{meters}}} = \frac{1000}{f_{\mathrm{mm}}}

Calculates lens bending strength in Diopters (D).

Adopted Sign Convention

  • f>0f > 0: Converging lens (bends rays together).
  • f<0f < 0: Diverging lens (spreads rays apart).
  • do>0d_o > 0: Real object (object is on input/left side).
  • do<0d_o < 0: Virtual object (converging rays incident on lens).
  • : Real image (image forms on output/right side).
  • di<0d_i < 0: Virtual image (image forms on input/left side).