🎓 Physics • Optics
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Spherical Mirror Calculator
Solves spherical mirror reflections 1/f = 1/d_o + 1/d_i with focal length f = R / 2.
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 Mirror Equation?
The mirror equation governs reflections from curved spherical surfaces, determining image location and magnification.
Formula & Step-by-Step Calculation
1/f = 1/d_o + 1/d_i, f = R / 2
Mirror equation with radius of curvature R.
Worked Step-by-Step Examples
Example 1
Concave mirror with f = 15 cm and object at 30 cm
Solution: d_i = 30 cm, M = -1.0 (Real, Same Size)
• 1/d_i = 1/15 - 1/30 = 1/30 ⟹ d_i = 30 cm
Common Real-World & Academic Use Cases
- ✓ Automotive side-view convex safety mirrors
- ✓ Astronomical reflecting telescopes
- ✓ Dental concave examination mirrors
How to Use the Spherical Mirror Calculator
1
Input Focal Length & Object Distance
Fill in cm.
2
Review Reflection
Inspect image distance and magnification.
Frequently Asked Questions
Q: Why are side mirrors convex?
Convex mirrors always form diminished virtual upright images with a wider field of view.