T TibCal

Focal Length Calculator

Calculate focal length calculator calculate lens focal length f and optical power P in Diopters from object distance do and image distance di (f = (do * di) / (do + di)). Accurate physics formulas and unit conversions for engineers, students & technicians.

Calculate Optical Focal Length (f = d_o ยท d_i / d_o + d_i)

Enter your physical parameters below to compute verified focal length metrics.

Distance from object to lens in cm (e.g. 30.0 cm).
Distance from image to lens in cm (+ for real, - for virtual).

Calculation Results

Primary Metric Output --
Metric Breakdown 1 --
Metric Breakdown 2 --
Metric Breakdown 3 --
Metric Breakdown 4 --
Metric Breakdown 5 --
Mathematical Standard --

Calculated using verified physical methodology: Gaussian Focal Length Formula: f = \d_o \cdot d_i / d_o + d_i
Optical Power: P = \100 / f_{\text{cm}} \text{ Diopters (dpt)}

*Note: Results represent system focal length and Diopter optical power.

Quick Summary

The Focal Length Calculator computes optical focal length ($f = \d_o \cdot d_i / d_o + d_i$) and lens power in Diopters ($P = 1/f_{\text{meters}}$) from object distance ($d_o$) and image distance ($d_i$).

Formula Explanation

Gaussian Focal Length Formula: f = \d_o \cdot d_i / d_o + d_i
Optical Power: P = \100 / f_{\text{cm}} \text{ Diopters (dpt)}

How It Works

The Focal Length Calculator multiplies object distance ($d_o$) by image distance ($d_i$) and divides by sum ($d_o + d_i$). It outputs focal length ($f$) in cm, mm, meters, optical power ($P$) in Diopters ($\text{dpt}$), linear magnification ($M = -d_i / d_o$), and lens type classification.

Step-by-Step Worked Example

Practical Problem: An optical bench setup places an object at $d_o = 30.0\text{ cm}$ and focuses a real image on a screen at $d_i = +15.0\text{ cm}$. Calculate system focal length $f$ and Diopter power $P$.

  1. Step 1: Identify Input Parameters: Object Distance $d_o = 30.0\text{ cm}$, Image Distance $d_i = +15.0\text{ cm}$.
  2. Step 2: Apply the Gaussian Product-over-Sum Formula: $f = \30.0 \times 15.0 / 30.0 + 15.0$.
  3. Step 3: Execute Numeric Multiplication & Division: $f = \450.0 / 45.0 = +10.00\text{ centimeters (cm)}$.
  4. Step 4: Convert to Millimeters & Meters: $f = 100.0\text{ mm} = 0.100\text{ meters}$.
  5. Step 5: Calculate Lens Power in Diopters ($P = 1/f_{\text{m}}$): $P = \1.0 / 0.10 = +10.00\text{ Diopters (dpt)}$. Magnification $M = -\15 / 30 = -0.50x$. Converging positive lens.

Real-World Calculation Examples

Scenario 1: Camera Lens Benchmark

Parameters: $d_o = 30\text{ cm}$, $d_i = +15\text{ cm}$

Result: $f = +10.00\text{ cm}$ ($+10.00\text{ dpt}$ power, 100mm focal length). Camera lens benchmark.

Scenario 2: Reading Magnifier Virtual Image

Parameters: $d_o = 6\text{ cm}$, $d_i = -15\text{ cm}$ (virtual image)

Result: $f = +10.00\text{ cm}$ ($+10.00\text{ dpt}$ power). Magnifying glass focal length.

Scenario 3: Projector Cinema Lens

Parameters: $d_o = 10.2\text{ cm}$, $d_i = +510\text{ cm}$ (5.1m screen)

Result: $f = +10.00\text{ cm}$ ($+10.00\text{ dpt}$ power). Cinema projector optics.

Scenario 4: Diverging Eye Prescription Concave Lens

Parameters: $d_o = 30\text{ cm}$, $d_i = -7.5\text{ cm}$

Result: $f = -10.00\text{ cm}$ ($-10.00\text{ dpt}$ power). Diverging myopia eyeglass focal length.

Key Benefits of Using This Calculator

Product-over-Sum Gaussian Solver

Solves system focal length ($f = \d_o d_i / d_o + d_i$) instantaneously without algebraic rearrangement.

Diopter Optical Power Output

Computes optical power ($P = 1/f_{\text{meters}}$) in Diopters ($\text{dpt}$) used in optometry.

Multi-Unit Readouts

Outputs focal length in cm, mm, meters, and Diopters ($\text{dpt}$).

100% Free & Client-Side

Executes locally in your browser with zero latency or web server transmission.

Frequently Asked Questions (FAQ)

What is focal length in optics?

Focal length (f) is the distance from the optical center of a lens or curved mirror to its principal focal point where parallel light rays converge (f = (do * di) / (do + di)).

What is the formula for focal length from object and image distances?

f = (do * di) / (do + di), derived from the Gaussian thin lens equation 1/f = 1/do + 1/di.

What is optical power in Diopters (dpt)?

Optical power P = 1 / f_meters is the reciprocal of focal length measured in meters (e.g. 0.25 m focal length = +4.0 Diopters).

How does focal length affect camera field of view?

Shorter focal lengths (e.g. 18mm, wide angle) yield wider fields of view; longer focal lengths (e.g. 200mm, telephoto) yield narrow, magnified fields of view.

What is the focal length of a flat plane glass pane?

Focal length f = infinity (power P = 0 Diopters).

How calculates focal length for a curved spherical mirror?

For spherical mirrors of radius R: f = R / 2.

What is effective focal length (EFL) of two thin lenses in contact?

1/f_total = 1/f1 + 1/f2 (or total power P_total = P1 + P2).

Why does a short focal length lens refract light more strongly?

A short focal length requires sharper surface curves, bending incoming parallel light rays more sharply to focus closer to the lens (higher Diopter power P).

How converts mm focal length to Diopters?

Power P = 1000 / f_mm (e.g. a 50mm camera lens has P = 1000 / 50 = +20.0 Diopters).

What is chromatic aberration?

Chromatic aberration occurs because refractive index n varies slightly with wavelength (dispersion), causing different colors of light to focus at slightly different focal lengths f.

Related Calculators