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Young's Double Slit Calculator

Find fringe spacing β = λD/d for double-slit interference

Parameters

nmⓘ
mⓘ
mmⓘ
Show Trail

Controls

xⓘ

Calculated Values

Fringe Spacing:
1.20;mm1.20;mm
Fringe Spacing:
1200.00;μm1200.00;μm

Examples

λ=600 nm, D=1 m, d=0.5 mm

Standard lab.

    Visualization

    Young's Double-Slit Interference

    Coherent light from two slits separated by d produces interference on a screen at distance D. Path difference Δ ≈ d y/D for small angles. Bright fringes when Δ = mλ; dark when Δ = (m + ½)λ.

    Fringe spacing β = λD/d is the distance between adjacent bright fringes (independent of m). Larger D or λ increases spacing; smaller slit separation d increases spacing.

    Typical lab: λ ≈ 600 nm (red laser), d ~ 0.5 mm, D ~ 1 m → β ≈ 1.2 mm. Requires spatial and temporal coherence.

    Intensity varies as cos²(πΔ/λ). Real slits have finite width, modulating envelope with single-slit diffraction.

    Foundation for understanding thin films, Michelson interferometer, and holography phase relationships.

    Key Concepts

    • β = λD/d
    • Bright: Δ = mλ
    • Dark: Δ = (m+½)λ
    • Coherent sources
    • Path difference Δ ≈ dy/D

    Real-World Applications

    • Interference demonstration
    • Measuring λ
    • Testing flatness (interferometry)
    • Class 12 Young experiment
    • Foundation for thin films

    Explore Further

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    • Spherical Mirror Equation

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    • Lens Power

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    • Critical Angle

      Find critical angle for total internal reflection between two media.

    Physics Equations

    Fringe Spacing:
    β=λDd\beta = \frac{\lambda D}{d}

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Fringe Spacing

    Equation:

    β=λDd\beta = \frac{\lambda D}{d}

    Explanation:

    β = separation between adjacent bright fringes.

    2

    Step 2: Values

    Result:

    λ=600nm,D=1m,d=0.5mmλ = 600 nm, D = 1 m, d = 0.5 mm
    3

    Step 3: Substitute

    Calculation:

    β=6.0000e−7×15.0000e−4=1.2000e−3 m\beta = \frac{6.0000e-7\times1}{5.0000e-4} = 1.2000e-3\text{ m}
    4

    Step 4: Result

    Result:

    β=1.2000mm=1200.00μmβ = 1.2000 mm = 1200.00 μm
    5

    Step 5: Path Difference

    Equation:

    Δ=dsin⁡θ≈dy/D\Delta = d\sin\theta \approx d y/D

    Explanation:

    Bright: Δ = mλ; dark: Δ = (m+½)λ.

    6

    Step 6: Coherence

    Requires coherent sources (single slit + double slit).

    Explanation:

    Class 12 wave optics experiment.

    Frequently Asked Questions (FAQ)

    Why single slit before double?

    Provides coherent wavefront from one source.

    White light fringes?

    Colored fringes; central white, orders overlap at large m.

    Practice MCQs

    1. Fringe spacing β =
    2. Red light vs blue, same setup:
    3. Double slit separation halved:
    4. Bright fringe condition:
    5. Coherence needed because:
    6. Screen farther (larger D):

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