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Thin Lens Equation Calculator

Find image distance v and magnification m from object distance u and focal length f

Parameters

cmⓘ
cmⓘ
Show Trail

Controls

xⓘ

Calculated Values

Image Distance:
30.00;cm30.00;cm
Magnification:
−1.00;-1.00;

Examples

u=30 cm, f=15 cm

Real image.

    Visualization

    Thin Lens 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).

    For a thin convex lens, object beyond 2f gives real inverted image between f and 2f. Object inside f gives virtual upright magnified image (magnifying glass).

    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.

    • Spherical Mirror Equation

      Calculate image position and magnification for concave and convex mirrors.

    • 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

    Lens 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: Lens Equation

    Equation:

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

    Explanation:

    Sign convention: u, v, f positive for real object/image with convex lens (Cartesian).

    2

    Step 2: Given

    Result:

    u=30cm,f=15cmu = 30 cm, f = 15 cm
    3

    Step 3: Solve for v

    Calculation:

    1v=1f−1u=115−130\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{15} - \frac{1}{30}

    Result:

    v=30.0000cmv = 30.0000 cm
    4

    Step 4: Magnification

    Equation:

    m=−v/um = -v/u

    Calculation:

    m=−(30.0000)/30=−1.0000m = -(30.0000)/30 = -1.0000

    Result:

    m=−1.0000m = -1.0000
    5

    Step 5: Image Nature

    Inverted image

    Explanation:

    |m| > 1 enlarged; |m| < 1 diminished.

    6

    Step 6: Ray Diagram

    Parallel ray → focal point; central ray undeviated.

    Explanation:

    Verify with three principal rays.

    Frequently Asked Questions (FAQ)

    Sign convention?

    Use consistent Cartesian or NCERT convention; this calculator uses u, f, v positive for standard real-object convex-lens cases.

    Thick lenses?

    Use lens maker equation; thin lens approximation when thickness << radii.

    u = f?

    Image at infinity; parallel emergent beam.

    Practice MCQs

    1. Lens equation:
    2. m = −v/u negative m means:
    3. Object at 2f gives image at:
    4. Power 2 D means f =
    5. Virtual image:
    6. Convex lens converges:

    Related Calculators

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

    Spherical Mirror EquationCalculate image position and magnification for concave and convex mirrors.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.