🎓 Physics • Optics
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Thin Lens Equation Calculator
Solves the Gaussian thin lens equation 1/f = 1/d_o + 1/d_i, calculating magnification and image type.
Thin Lens & Curved Mirror Equation
Gaussian formula: 1/f = 1/dₒ + 1/dᵢ and magnification M = -dᵢ/dₒ.
Optical System Presets:
(+ Converging, - Diverging)
Distance to lens / mirror
Upright height
Geometric Optical Ray DiagramReal (Inverted), Diminished
Image Distance (dᵢ)
16.67 cm
Magnification (M)
0.67×
Inverted (M < 0)
Optical Power
10.00 D
Converging (Positive)
Step-by-Step Optical Analysis
1. Gaussian Equation: 1/f = 1/dₒ + 1/dᵢ
2. Solve for Image Distance: dᵢ = (f · dₒ) / (dₒ - f)
3. Substitution: dᵢ = (10 × 25) / (25 - 10) = 16.67 cm
4. Magnification: M = -dᵢ / dₒ = -0.67×
5. Image Height: hᵢ = M × hₒ = -3.33 cm
6. Optical Power (Lens): P = 1 / f(m) = 100 / 10 = 10.00 Diopters (D)
What is the Thin Lens Equation?
The thin lens equation relates focal length, object distance, and image distance for converging (convex) and diverging (concave) lenses.
Formula & Step-by-Step Calculation
1/f = 1/d_o + 1/d_i, M = -d_i / d_o
Gaussian lens formula and magnification.
Worked Step-by-Step Examples
Example 1
Object at 25 cm with converging lens of f = 10 cm
Solution: Image distance d_i = 16.67 cm, M = -0.67 (Real, Inverted)
• 1/d_i = 1/10 - 1/25 = 3/50 ⟹ d_i = 16.67 cm
Common Real-World & Academic Use Cases
- ✓ Camera lens focal positioning
- ✓ Eyeglass prescription diopters
- ✓ Microscope and telescope design
How to Use the Thin Lens Equation Calculator
1
Enter Focal Length f
Input cm (+ for convex, - for concave).
2
Enter Object Distance d_o
Input distance in cm.
3
Inspect Image
View image distance, magnification, and real/virtual status.
Frequently Asked Questions
Q: What does a negative image distance mean?
A negative d_i indicates a virtual image located on the same side of the lens as the object.