Monochromatic light of wavelength 530 nm passes through a horizontal single slit of width \(1.5 \mu \mathrm{m}\) in an opaque plate. A screen of dimensions \(2.0 \mathrm{m} \times 2.0 \mathrm{m}\) is \(1.2 \mathrm{m}\) away from the slit. (a) Which way is the diffraction pattern spread out on the screen? (b) What are the angles of the minima with respect to the center? (c) What are the angles of the maxima? (d) How wide is the central bright fringe on the screen? (e) How wide is the next bright fringe on the screen?

When monochromatic light passes through a small slit, it doesn't simply travel in straight lines; instead, it bends and spreads out. This bending and spreading of light is known as diffraction, and the resulting band of light and dark areas is called the diffraction pattern. In our exercise, a horizontal single slit causes the light to form a diffraction pattern that spreads horizontally across the screen. To visualize this, imagine water waves hitting a narrow barrier with a slit; the waves spread out in a semi-circular pattern on the other side, similar to how light creates a diffraction pattern on the screen.

The diffraction pattern consists of a central bright fringe, where the light waves constructively interfere, surrounded by alternating dark and bright fringes. The dark areas are the result of destructive interference, where waves cancel each other out. Understanding the diffraction pattern helps us predict where light will be most intense and where it will be absent, which is essential for applications like optical instruments and engineering designs.

The angle of minima in a single-slit diffraction pattern represents the direction where the destructive interference occurs, creating dark bands on the screen. Mathematically, these angles can be found using the formula
\( m \lambda = w \sin{\theta} \)
where m is an integer (1, 2, 3,...) denoting the order of the minimum, \lambda is the wavelength of the light, w is the width of the slit, and \theta is the angle of minima with respect to the center of the diffraction pattern. By measuring these angles, or calculating them with the given wavelength and slit width, we can determine where the dark bands will appear on the screen, and this helps in predicting the overall shape and spacing of the diffraction pattern.

Conversely, the angle of maxima reflects where in the diffraction pattern we expect to see the bright fringes due to constructive interference. The equation to find the angle of maxima is subtly different from that of the minima:
\((m +\frac{1}{2})\lambda = w \sin{\theta}\)
Here, m is again an integer (0, 1, 2,...), but for maxima, we add a half before multiplying by the wavelength. By calculating the angle of maxima, we can pinpoint the location of bright bands on the screen. These bright fringes are indicative of points where light waves reinforce each other, strengthening the overall intensity of the light.

The central bright fringe is the hallmark of the single-slit diffraction pattern, located at the center of the pattern and invariably the brightest and widest band. This band is created by the direct beams of light that pass through the slit without being deflected. It is symmetrical and is usually used as a reference point for measuring the position of other fringes. Its width directly influences the spacing of subsequent bright and dark bands. In our exercise, we determine this width by finding the distance from the center to the first minimum on either side of the central maximum, which helps us understand just how much the light spreads out and how it relates to the slit width and wavelength.