Single-Slit Diffraction and the Limit of Resolution

For uniform monochromatic illumination in the far field, a slit much wider than the wavelength gives a bright central maximum between its first minima and weaker side maxima. At small angles its width is approximately W = 2 lambda D/a, where a is slit width and D screen distance. At fixed wavelength and distance, narrowing a while it stays much wider than lambda increases W. Wavefront parts interfere after the opening; this is not the slit's geometrical shadow.

At fixed slit width and screen distance, a longer wavelength produces a broader central maximum. In the same medium, red light has a longer wavelength than violet, so red gives the broader pattern. This comparison holds the slit and observation geometry fixed.

Two identical finite slits under coherent illumination give interference fringes inside a single-slit diffraction envelope. Near a distant screen's centre, interference spacing is approximately equal, but fringe brightness varies with the envelope. A single slit has no two-slit interference modulation. Regularity alone does not identify two slits: gratings can also give regularly spaced principal maxima.

An aperture spreads each point image into a diffraction pattern. For two equally bright point sources and an ideal circular aperture, the Rayleigh criterion calls them just resolved when one pattern's centre lies at the other's first minimum. At fixed wavelength, a larger aperture narrows this blur and lowers the angular threshold. Atmospheric blur and optical defects can impose other limits.

For small angles on a distant screen, single-slit central width W is approximately 2 lambda D/a, where a is slit width and D screen distance. With a and D fixed, multiplying wavelength by a factor multiplies W by that factor. This is a width approximation, not a statement that every feature keeps the same intensity.

When wavelength and slit width both change, compare their ratio: W is proportional to lambda/a at fixed screen distance and small angles. The new width divided by the old width equals the wavelength factor divided by the slit-width factor. Equal factors cancel, so changing both by the same factor leaves the width unchanged.

This ratio method compares widths. It does not draw the diffraction pattern.

For an ideal circular aperture, the small-angle Rayleigh threshold is 1.22 lambda/B radians, with B the aperture diameter. Compare the source separation with this threshold: equality is just resolved; larger separation satisfies the criterion. Doubling B at fixed wavelength halves the threshold. This prediction applies when diffraction, rather than atmosphere or defects, limits the image.