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What Is Diffraction? Find a Single-Slit Width and Minimum Angle

Using the far-field condition for single-slit minima, the slit width is 1.56 μm and the first dark minimum occurs at 20.7° from the central axis.

Question

Monochromatic visible light with wavelength 550 nm550\,\mathrm{nm} passes through a single slit. In the far-field diffraction pattern, the second minimum occurs at 45.0∘45.0^\circ from the incident direction.

  1. Find the slit width.
  2. Find the angle of the first minimum.

Answer

Diffraction is the spreading of a wave after it passes through an opening or around an edge. For a single slit in the far field, dark minima satisfy

asin⁡θm=mλ,m=1,2,3,…a\sin\theta_m=m\lambda, \qquad m=1,2,3,\ldots

For the second minimum,

a=2(550×10−9 m)sin⁡45.0∘=1.56×10−6 m=1.56 μm.a=\frac{2(550\times10^{-9}\,\mathrm{m})}{\sin45.0^\circ} =1.56\times10^{-6}\,\mathrm{m} =1.56\,\mu\mathrm{m}.

For the first minimum,

sin⁡θ1=550×10−91.56×10−6=0.354,\sin\theta_1 =\frac{550\times10^{-9}}{1.56\times10^{-6}} =0.354,

so

θ1=20.7∘.\theta_1=20.7^\circ.

Thus the slit is approximately 1.56 μm1.56\,\mu\mathrm{m} wide, and the first dark minimum lies at 20.7∘20.7^\circ on either side of the central axis.

Evidence boundary

The result uses Fraunhofer single-slit diffraction for monochromatic light and interprets the stated ‘second minimum’ as order m = 2. It locates ideal dark minima; finite screen distance, imperfect coherence, slit-thickness effects, and intensity away from the minima are outside the calculation.

Sources

These references support the concepts and methods used in the explanation above.

What Is Diffraction? Single-Slit Calculation | Verla