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Diffraction Grating Calculator

Find diffraction angle θ from slit spacing d, wavelength λ, and order m

Parameters

μmⓘ
nmⓘ
ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Diffraction Angle:
15.96;°15.96;°

Examples

m=1, λ=550 nm, d=2 μm

First order.

    Visualization

    Diffraction Grating

    A diffraction grating has many parallel slits separated by distance d. Constructive interference for wavelength λ at order m satisfies d sin θ = mλ (m = 0, ±1, ±2, …).

    Each order appears at a different angle; white light produces a spectrum. Resolving power R = λ/Δλ = Nm where N is number of illuminated slits.

    Grating spacing is often given as lines per mm: d = 1/(lines/mm × 1000). Example: 500 lines/mm → d = 2 μm.

    Compared to double slit, grating gives sharper maxima and better wavelength resolution for spectroscopy.

    Condition |sin θ| ≤ 1 limits observable orders; higher m disappears at long λ or small d.

    Key Concepts

    • d sin θ = mλ
    • Orders m = 0, ±1, ±2…
    • R = Nm
    • Spectral separation
    • |mλ/d| ≤ 1

    Real-World Applications

    • Spectrometers
    • CD/DVD diffraction colors
    • Astronomical spectroscopy
    • Wavelength calibration
    • Class 12 wave optics

    Explore Further

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    • 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

    Grating:
    dsin⁡θ=mλd\sin\theta = m\lambda

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Grating Equation

    Equation:

    dsin⁡θ=mλd\sin\theta = m\lambda

    Explanation:

    m = 0, ±1, ±2, … order; d = slit spacing.

    2

    Step 2: Convert Units

    Calculation:

    d=2 μm=2.0000e−6 m,λ=550 nmd = 2\,\mu\text{m} = 2.0000e-6\text{ m}, \quad \lambda = 550\text{ nm}
    3

    Step 3: sin θ

    Calculation:

    sin⁡θ=mλd=1×5.5000e−72.0000e−6=0.275000\sin\theta = \frac{m\lambda}{d} = \frac{1\times5.5000e-7}{2.0000e-6} = 0.275000
    4

    Step 4: Angle

    Result:

    θ=15.9620°θ = 15.9620°
    5

    Step 5: Orders

    Multiple bright fringes at different m.

    Explanation:

    Higher m → larger angle; white light gives spectra.

    6

    Step 6: Resolving Power

    Equation:

    R=NmR = Nm

    Explanation:

    N = number of illuminated slits.

    Frequently Asked Questions (FAQ)

    vs double slit?

    Grating has many slits → narrower bright fringes, better resolution.

    No solution for θ?

    |mλ/d| > 1 → that order does not exist.

    Practice MCQs

    1. Grating equation:
    2. Higher order m means:
    3. More slits N gives:
    4. m = 0 order is:
    5. d doubles, same λ and m:
    6. White light through grating:

    Related Calculators

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

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