The first two dark fringes on one side of the central...

The first two dark fringes on one side of the central maximum in a single-slit diffraction pattern are $1.0 \mathrm{~mm}$ apart. The wavelength of the light is $610 \mathrm{~nm}$ and the screen is $1.0 \mathrm{~m}$ from the slit. What is the slit width?

Key Concepts

Interference Patterns

Interference patterns are the result of the superposition of waves that can either constructively or destructively interfere. In the context of single-slit diffraction, the interference leads to a central bright maximum flanked by successive dark and less intense bright fringes, which can be analyzed to deduce physical properties such as the width of the slit.

Single-Slit Diffraction

This concept explains how light spreads out after passing through a narrow opening, generating a pattern of bright and dark regions on a screen. The pattern arises due to the interference between wavefronts emanating from different parts of the slit, with the dark fringes representing points of destructive interference.

Dark Fringe Condition

In single-slit diffraction, dark fringes (minima) occur at angles where the path difference between light from the different parts of the slit results in complete destructive interference. Mathematically, this is expressed as a?sin? = m?, where 'a' is the slit width, '?' is the angle relative to the central axis, '?' is the wavelength, and 'm' is an integer (excluding zero).

Small-Angle Approximation

Often, the diffraction angles are small enough that sin? can be approximated by tan?, which is further approximated by the ratio of the fringe displacement to the screen distance (y/L). This simplification allows linear relations between the position of the fringes on the screen and the diffraction parameters like slit width and wavelength.

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