PhysicsSolver360 logoPhysicsSolver360°
Powered by Solver360°

Lens Power Calculator

Find power P = 1/f and combined power of two thin lenses in contact

Parameters

mⓘ
mⓘ
Show Trail

Controls

xⓘ

Calculated Values

Power 1:
5.00;D5.00;D
Power 2:
4.00;D4.00;D
Total Power:
9.00;D9.00;D
Equivalent f:
0.11;m0.11;m

Examples

f₁=0.2 m, f₂=0.25 m

Contact lenses.

    Visualization

    Lens Power and Combination

    Lens power P = 1/f when focal length f is in meters. Unit: diopter (D). A +2 D converging lens has f = 0.5 m = 50 cm. Negative power indicates diverging lens.

    Thin lenses in contact combine additively: P_total = P₁ + P₂, so 1/f_eq = P₁ + P₂. Eyeglass prescriptions often sum distance and cylinder powers for compound lenses.

    Converting: f (cm) = 100/P if P in diopters. Two +1 D lenses in contact behave like one +2 D lens.

    Lens maker equation for thick lenses: 1/f = (n−1)(1/R₁ − 1/R₂) accounts for refractive index and radii of curvature.

    Applications: correcting myopia (negative P), hyperopia (positive P), and designing camera objectives from multiple elements.

    Key Concepts

    • P = 1/f (f in m)
    • Diopter D = m⁻¹
    • P_total = P₁ + P₂ (contact)
    • Convex P > 0
    • Concave P < 0

    Real-World Applications

    • Eyeglass prescriptions
    • Contact lenses
    • Compound camera lenses
    • Microscope objectives

    Explore Further

    More optics tools

    Physics Equations

    Power:
    P=1fP = \frac{1}{f}
    Combined:
    Ptotal=P1+P2P_{total} = P_1 + P_2

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Lens Power

    Equation:

    P=1f(diopters, D)P = \frac{1}{f} \quad (\text{diopters, D})

    Explanation:

    f in meters: 1 D = 1 m⁻¹.

    2

    Step 2: Individual Powers

    Calculation:

    P1=1/0.2=5.0000 D,P2=1/0.25=4.0000 DP_1 = 1/0.2 = 5.0000\text{ D}, \quad P_2 = 1/0.25 = 4.0000\text{ D}
    3

    Step 3: Combined (thin lenses in contact)

    Equation:

    Ptotal=P1+P2P_{total} = P_1 + P_2

    Calculation:

    P=5.0000+4.0000=9.0000 DP = 5.0000 + 4.0000 = 9.0000\text{ D}

    Result:

    Ptotal=9.0000DP_total = 9.0000 D
    4

    Step 4: Equivalent Focal Length

    Calculation:

    feq=1/P=0.1111 mf_{eq} = 1/P = 0.1111\text{ m}

    Result:

    feq=0.1111mf_eq = 0.1111 m
    5

    Step 5: Sign

    Convex/converging: P > 0; concave/diverging: P < 0.

    Explanation:

    Eyeglass prescription uses diopters.

    6

    Step 6: Note

    Separated lenses need more advanced formula.

    Explanation:

    This calculator assumes contact or thin-lens sum.

    Frequently Asked Questions (FAQ)

    Prescription +2.5 D?

    Converging lens, f ≈ 40 cm.

    Separated lenses?

    Use lens combination formula with separation; not simple sum.

    Practice MCQs

    1. 1 D equals focal length:
    2. +3 D lens is:
    3. Two +2 D in contact:
    4. f = 25 cm → P =
    5. Negative power lens:
    6. SI unit of power:

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