# Diffraction Of Monochromatic Light

Diffraction happens when a wave hits an obstacle or gap, diffraction is greatest when the gap is about the same size as the wavelength of the wave. The waves bend round the object or spread out when they pass through the gap, this is called diffraction.

Single Slit Diffraction

Diffraction of monochromatic light with wavelength. From a series of apertures with a spacing d G. The angled lines indicate regions of constant phase while arrows denote directions of intensity peaks in the diffraction pattern. Due to diffraction, the reflected light spreads, and if the facet is small enough, only part of the reflected (and diffracted) light enters the eye and is focused onto the retina. From the center of the reflected pencil of light outwards, the sequence of colours will be similar to that shown above for a circular aperture.

When monochromatic laser light is shone through a narrow single slit a diffraction pattern is produced consisting of light and dark fringes. It produces a wide central bright fringe. The other bright fringes get dimmer as you move away from the centre.

Diffraction grating.

A diffraction grating is a piece of glass with lots of closely spaced parallel lines on it each of which allows light to pass through it, this is a transmission diffraction grating.

Diffraction gratings are used in spectrometers. The diffraction grating splits up the light into a spectra.

d = grating spacing in metres (m)
J = angle of diffraction
n = order number
l = wavelength on the light in metres (m)

This equation can be rearranged to

If there are N lines per metre on a diffraction grating then d can be calculated using

## Diffraction Grating Of Monochromatic Light

Diffraction gratings are used in the spectral analysis of light from stars.

#### Line Spacing Calculations from Diffraction Gratings

By definition, a diffraction grating is composed of a planar substrate containing a parallel series of linear grooves or rulings, which can be transparent, semi-transparent, or opaque. When the spacing between lines on a diffraction grating is similar in size to the wavelength of light, an incident collimated and coherent light beam will be strongly diffracted upon encountering the grating. This interactive tutorial examines the effects of wavelength on the diffraction patterns produced by a virtual periodic line grating of fixed line spacing.

The tutorial initializes with a beam of coherent and collimated purple monochromatic light (400 nanometers) incident on a periodic diffraction grating. Upon passing through the line grating, the light beam is diffracted into a bright central band (zeroth-order) on the detector screen, flanked by several higher-order (1st, 2nd, and 3rd) diffraction bands or maxima. In order to operate the tutorial, use the Wavelength slider to adjust the size of monochromatic light passing through the grating in a range between 400 and 700 nanometers. As the slider is translated to the right, the wavelength of incident light increases, producing a corresponding change to the diffraction pattern observed on the detector screen (the long, horizontal line above the slider). The diffraction bands formed by the higher-order maxima identify the diffraction angles in which wavefronts having the same phase become reinforced as bright areas due to constructive interference. In regions between the diffraction bands, the wavefronts are out of phase and cancel the intensity of each other by destructive interference.

## Monochromatic Light Diffraction

The zeroth-order central maximum band is formed from light waves that do not become diffracted when passing through the diffraction grating, and displays an intensity value only slightly reduced from that of the incident beam. The diffraction angle, which is identified by the symbol q, is the determined by the angle subtended by the zeroth and first-order bands on the detector with respect to the grating. A right triangle containing the diffraction angle at the detector screen is congruent with another triangle at the grating defined by the wavelength of illumination (l) and the spacing between rulings (d) on the grating according to the equation:

sin (q) = l/d

As a result, the reinforcement of diffraction bands or spots occurs at locations having an integral number of wavelengths (l, 2l, 3l, etc.) because the diffracted wavefronts arrive at these locations in phase and are able to reinforce each other through constructive interference. If the sine of the diffraction angle is calculated from the distance between diffraction bands on the detector screen and between the screen and the line grating, the spacing (d) between individual rulings on the grating can be determined using the grating equation in the form:

ml = d • sin (q)

where l is the wavelength of incident light and m is an integral number of diffraction bands. For example, calculations based on the distance between the first and zeroth order diffraction bands require the value of m to be 1, whereas similar calculations between the zeroth and second order diffraction bands have a value of m equal to 2, and so on. According to the equation, the size of the diffraction angle decreases as the line grating space intervals increase. Likewise, longer wavelengths give rise to larger diffraction angles at constant line grating spacings.

The effect of wavelength can be demonstrated by illuminating the line grating with white light (containing a mixture of all colors). Under these conditions, the zeroth-order diffraction band appears white, but higher order bands display an elongated spectrum of colors with blue being closest to the zeroth-order band. Thus, blue light is diffracted to a lesser extent than is green or red light, as illustrated in the tutorial.

## Why Monochromatic Light Is Used In Diffraction

Contributing Authors

Douglas B. Murphy - Department of Cell Biology and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205.

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

Matthew J. Parry-Hill and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.