This experiment involves studying the diffraction patterns produced when a coherent 635 nm laser beam passes through a narrow single slit or is diffracted by a human hair. The purpose is to investigate the wave-like behavior of light and apply diffraction theory to measure physical quantities like slit width and hair diameter.

 Wave Nature of Light

Light exhibits particle and wave-like properties, depending on the experimental conditions. In this experiment, we focus on the wave nature of light, specifically the diffraction phenomenon. Diffraction occurs when a wave encounters an obstacle or aperture, causing it to bend and spread. When light passes through a narrow slit or around an object like a hair, the light waves interfere, forming a diffraction pattern on a distant screen.

 At specific angles to either side, destructive interference occurs, creating dark bands, or minima, in the pattern. Beyond the central maximum, alternating bright and dark fringes (maxima and minima) are observed, decreasing in intensity as the angle from the center increases.

The positions of these minima in the diffraction pattern can be described by the following condition for destructive interference:

where:

• a is the width of the slit,

• θ is the angle from the centerline of the diffraction pattern to the m-th minimum (dark fringe),

• λ is the wavelength of the laser light (635 nm),

• m is an integer representing the order of the minimum (e.g., 1, 2, 3, …).

The diffraction pattern consists of a central bright maximum, twice as wide as the other maxima, and successively dimmer bright fringes separated by dark bands. The location of the minima can be measured, and the corresponding slit width can be determined using the above equation.

 Intensity Distribution of Single-Slit Diffraction

The intensity distribution of light across the screen follows a pattern governed by both diffraction and interference. The intensity I(θ) as a function of angle θ is given by:

where:

• I0 is the intensity at the central maximum,

• a is the slit width,

• λ is the wavelength of the light,

• θ is the diffraction angle.

The intensity falls off rapidly as the angle increases, with the central maximum being the brightest.

Hair Diffraction as a Narrow Obstacle

When a thin object like a human hair is placed in the path of the laser beam, it acts as a barrier, causing the light to diffract around it. This diffraction also produces a pattern of alternating bright and dark fringes on a screen, similar to single-slit diffraction. The diffraction pattern from a hair is related to its diameter, which can be treated as the slit width in the diffraction equation. The dark fringes in the pattern correspond to points of destructive interference, where the light waves diffracted around the hair cancel each other out.

The condition for destructive interference in this case is also given by:

where:

• d is the diameter of the hair,

• θ is the angle corresponding to the m-th dark fringe.

The hair diameter can be calculated by measuring the fringe spacing and knowing the distance between the hair and the screen.

 Measurement of Fringe Spacing

In the experiment, the diffraction pattern is projected onto a screen positioned at a known distance L from the slit or the hair. The distance between adjacent dark fringes (fringe spacing y) is measured. For small angles, where sin⁡θ≈θ≈y/L, the slit width (or hair diameter) can be approximated by:

where:

• d is the diameter of the hair,

• m is an decimal representing the order of the minimum plus 0.5(e.g.,  m=1+0.5, 2+0.5, 3+0.5...)

• λ is the wavelength of the laser (650 nm),

• L is the distance from the hair to the screen,

• y is the fringe spacing (distance between adjacent bright fringes).