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Telescope Magnification Calculator

Find angular magnification M = f_o / f_e for normal adjustment

Parameters

cmⓘ
cmⓘ
Show Trail

Controls

xⓘ

Calculated Values

Magnification:
10.00;×10.00;×
Tube Length (approx):
110.00;cm110.00;cm

Examples

f_o=100, f_e=10

10× telescope.

    Visualization

    Telescope Angular Magnification

    An astronomical refracting telescope in normal adjustment (relaxed eye, final image at infinity) has angular magnification M = f_o/f_e, where f_o is objective focal length and f_e is eyepiece focal length.

    Large M requires long objective (high f_o) and short eyepiece (small f_e). Tube length L ≈ f_o + f_e. Objective diameter sets light-gathering and resolution, not M directly.

    Example: f_o = 100 cm, f_e = 2 cm → M = 50×. Field of view decreases as M increases. Terrestrial telescopes add erecting prisms; magnification formula may include sign conventions.

    Reflecting telescopes use curved mirrors with same M concept for eyepiece combination. Newtonian, Cassegrain designs fold optical path.

    Magnifying glass alone: M ≈ 1 + D/f_e (D = near point). Compound microscope uses different formula M ≈ (L/f_o)(D/f_e).

    Key Concepts

    • M = f_o/f_e
    • Normal adjustment L ≈ f_o + f_e
    • Large f_o → high M
    • Objective sets brightness/resolution
    • Eyepiece sets magnification

    Real-World Applications

    • Astronomical telescopes
    • Binoculars (with prisms)
    • Spotting scopes
    • Class 12 optical instruments
    • Amateur astronomy

    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.

    • 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.

    Physics Equations

    Magnification:
    M=fofeM = \frac{f_o}{f_e}

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Angular Magnification

    Equation:

    M=fofeM = \frac{f_o}{f_e}

    Explanation:

    Astronomical telescope in normal adjustment.

    2

    Step 2: Focal Lengths

    Result:

    fo=100cm,fe=10cmf_o = 100 cm, f_e = 10 cm
    3

    Step 3: Magnification

    Calculation:

    M=10010=10.0000M = \frac{100}{10} = 10.0000

    Result:

    M=10.00×M = 10.00×
    4

    Step 4: Tube Length

    Equation:

    L≈fo+feL \approx f_o + f_e

    Calculation:

    L≈110cmL \approx 110 cm

    Explanation:

    Normal adjustment: final image at infinity.

    5

    Step 5: Brightness

    Magnification reduces field of view.

    Explanation:

    Large f_o improves light gathering.

    6

    Step 6: Terrestrial Telescope

    Uses erecting prism; different M formula.

    Explanation:

    This tool is for simple astronomical layout.

    Frequently Asked Questions (FAQ)

    Maximum practical M?

    Limited by atmosphere, vibration, and field; very high M dims and blurs.

    Binoculars 10×50?

    10× magnification, 50 mm objective diameter.

    Practice MCQs

    1. Telescope M =
    2. To increase M:
    3. Normal adjustment means:
    4. f_o=80 cm, f_e=4 cm → M =
    5. Objective diameter affects:
    6. Microscope M differs because:

    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.Lens PowerConvert focal length to diopters and combine thin lens powers.Critical AngleFind critical angle for total internal reflection between two media.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.