💡 Sign convention (New Cartesian)
Object distance u → negative for real object. Image distance v → positive for real image, negative for virtual. Focal length f → negative for concave mirror, positive for convex. Mirror formula: 1/f = 1/v + 1/u. Focal length and radius: f = R/2.
Mirror calculators
Formula, f = R/2, magnification, number of images
Solve for
Focal length (f)
Object distance (u)
same unit
Result
—
Radius of curvature (R)
Focal length f = R/2
—
Image distance (v)
Object distance (u)
same unit
Magnification m = −v/u
—
Angle between mirrors θ (°)
degrees
Number of images (n = 360°/θ − 1 when integer)
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🪞 Ray diagram
🧮Step-by-Step Solution▼ Show
| Concept | Formula | Notes / Sign convention |
|---|---|---|
| Laws of reflection | i = r | Incident ray, reflected ray, normal in same plane |
| Mirror formula (spherical) | 1/f = 1/v + 1/u | Cartesian sign convention |
| Focal length & radius | f = R/2 | R = radius of curvature |
| Magnification | m = hᵢ/hₒ = −v/u | m < 0 → inverted, m > 0 → erect |
| Number of images (two mirrors at θ) | n = 360°/θ − 1 | When 360/θ is integer |
About reflection and mirrors
For spherical mirrors the mirror formula is 1/f = 1/v + 1/u. Focal length is half the radius of curvature: f = R/2. Magnification m = −v/u; m < 0 means inverted, m > 0 erect. For two plane mirrors inclined at angle θ, when 360°/θ is an integer the number of images is n = 360°/θ − 1.