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Spherical Mirror Equation Calculator

Find image distance and magnification using 1/f = 1/u + 1/v

Parameters

cmⓘ
cmⓘ
Show Trail

Controls

xⓘ

Calculated Values

Image Distance:
23.08;cm23.08;cm
Magnification:
−0.92;-0.92;

Examples

u=25, f=12

Concave mirror.

    Visualization

    Spherical Mirror Equation

    Geometric optics treats light as rays obeying reflection and refraction laws. For thin lenses and spherical mirrors, the Gaussian lens/mirror equation 1/f = 1/u + 1/v relates object distance u, image distance v, and focal length f (all measured from the optical element, with sign conventions).

    Magnification m = −v/u compares image height to object height; negative m means inverted image. Real images form where light actually converges (v > 0 for lenses in standard convention); virtual images appear behind the element (v < 0).

    Concave mirrors (f > 0) form real inverted images for objects beyond C; convex mirrors always give virtual upright diminished images.

    Ray tracing uses three principal rays: parallel to axis → through focus; through center → undeviated; through focus → emerges parallel. Combined with the equation, this predicts image position, size, and orientation for cameras, eyes, microscopes, and projectors.

    Class 12 NCERT Ray Optics covers lenses, mirrors, power in diopters P = 1/f (f in meters), and combination of thin lenses in contact: P_total = P₁ + P₂.

    Key Concepts

    • 1/f = 1/u + 1/v
    • m = −v/u
    • P = 1/f (diopters)
    • f = R/2 for mirrors
    • Real vs virtual image
    • Principal ray construction

    Real-World Applications

    • Cameras and smartphone lenses
    • Eyeglasses and contact lenses
    • Microscopes and telescopes
    • Concave/convex mirrors in vehicles
    • Class 12 ray optics problems

    Explore Further

    More optics tools

    • Snell's Law

      Calculate refraction angles and analyze light behavior at media boundaries.

    • Magnification

      Calculate linear and angular magnification for optical systems.

    • Thin Lens Equation

      Find image distance and magnification using 1/f = 1/u + 1/v.

    • Lens Power

      Convert focal length to diopters and combine thin lens powers.

    • Critical Angle

      Find critical angle for total internal reflection between two media.

    • Diffraction Grating

      Calculate diffraction angles using d sin θ = mλ.

    Physics Equations

    Mirror Equation:
    1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}
    Magnification:
    m=−vum = -\frac{v}{u}

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Mirror Equation

    Equation:

    1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

    Explanation:

    Same form as lens; f = R/2 for spherical mirrors.

    2

    Step 2: Values

    Result:

    u=25cm,f=12cm(concave:f>0)u = 25 cm, f = 12 cm (concave: f > 0)
    3

    Step 3: Image Distance

    Calculation:

    v=ufu−f=25×1225−12v = \frac{uf}{u-f} = \frac{25\times12}{25-12}

    Result:

    v=23.0769cmv = 23.0769 cm
    4

    Step 4: Magnification

    Equation:

    m=−v/um = -v/u

    Result:

    m=−0.9231m = -0.9231
    5

    Step 5: Real vs Virtual

    Real image (screen)

    Explanation:

    Concave mirror: object beyond C gives real inverted image.

    6

    Step 6: Focal Length

    Equation:

    f=R/2f = R/2

    Explanation:

    Radius of curvature R = 2f.

    Frequently Asked Questions (FAQ)

    Convex vs concave?

    Concave converges; convex diverges.

    Why same equation as lens?

    Paraxial reflection law gives identical Gaussian form.

    Practice MCQs

    1. Concave mirror f is:
    2. f = R/2 means R = 24 cm gives f =
    3. Convex mirror image is always:
    4. Same as lens equation:
    5. Object at focus of concave mirror:
    6. Magnification |m| < 1 for convex mirror means:

    Related Calculators

    These tools connect to the same physics concepts used in this calculator.

    Thin Lens EquationFind image distance and magnification using 1/f = 1/u + 1/v.Lens PowerConvert focal length to diopters and combine thin lens powers.Critical AngleFind critical angle for total internal reflection between two media.Diffraction GratingCalculate diffraction angles using d sin θ = mλ.Wave PropertiesCalculate wavelength, frequency, amplitude, and wave velocity.Related Waves topic.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Quantum Harmonic OscillatorCalculate energy levels, wavefunctions, and quantum properties of harmonic oscillators.Related Modern Physics topic.