The diffracted waves then interfere with each other. Where crests meet or troughs meet there is reinforcement (constructive interference) – where a crest and tough meet there is cancellation (destructive interference). This results in only the ‘orders’ of light being viewed.

Grating equationcalculator

An airy pattern is a characteristic diffraction pattern that appears when coherent light passes through a circular aperture or lens, showing a central bright region surrounded by concentric dark and bright rings. This pattern is a direct result of the wave nature of light and the principles of diffraction, particularly the interference of light waves emanating from different points in the aperture. The airy pattern is significant in understanding optical imaging systems and the resolution limits of lenses.

When a parallel beam of monochromatic light is directed normally (at right angles to it!) at a diffraction grating, light is transmitted by the grating in certain directions only.

Reflectiongrating equation

A mathematical function that describes how a point source of light is distributed in an imaging system, directly related to the airy pattern observed in optical systems.

the diffracted light waves from adjacent slits reinforce each other in certain directions only, including the incident light direction, and cancel out in all other directions.

Therefore the perpendicular distance QY from the slit to the wavefront is equal to nλ , where λ is the wavelength of the light waves.

Grating equationderivation

For a given order and wavelength, the smaller the value of d, the greater the angle of diffraction. In other words, the larger the number of slits per metre, the bigger the angle of diffraction.

Grating equationwavelength

Click onto the image to go to an excellent site that explains this in even more detail and allows you to explore diffraction via an interactive activity.

Grating equationpdf

The effect is to form a new wavefront PYZ which travels in a certain direction and contributes to the first order diffracted beam.

The diffraction grating is an immensely useful tool for the separation of the spectral lines associated with atomic transitions. It separates the different colors of light much more than the dispersion effect in a prism is able to - it uses diffraction not refraction to do it!

Diffractiongrating equationderivation

The hydrogen gas in a thin glass tube is excited by an electrical discharge, the electrons are promoted by electrical energy into higher energy states - an then as they fall back to ground state some of the transitions result in photons in the visible region being emitted. This visible spectrum can be viewed through the grating.

It is excellent at separating the colors in incident light because different wavelengths are diffracted at different angles, according to the grating relationship:

A transmission diffraction grating is a slide with large number of parallel, closely spaced slits (transparent spaces) drawn on it. Early ones were carbon covered glass slides etched by a needle point - now they tend to be printed onto a slide.

For example, in the diagram, the wavefront emerging at P reinforces the wavefront emitted from Q one cycle earlier, which reinforces the wavefront emitted from R one cycle earlier, etc.

The condition for maximum intensity is the same as that for the double slit or multiple slits, but with a large number of slits the intensity maximum is very sharp and narrow, providing the high resolution for spectroscopic applications. The peak intensities are also much higher for the grating than for the double slit.

Grating equationexample

Diffractiongrating equation

When monochromatic light (light of a single wavelength - like the 632.8 nm red light from a helium-neon laser) strikes a diffraction grating it is diffracted to each side in multiple orders. The condition for maximum intensity is the same as that for a double slit. However, angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating.

To find the maximum number of orders produced, substitute θ = 90 ° (sinθ = 1) in the grating equation and calculate n using n = d/λ .

Note that from the equation you can see that, the bigger the wavelength the more diffraction. This means that it is the red end of the visible spectrum that is diffracted the most. In the prism the red end of the spectrum is refracted the least!

Since the angle of diffraction of the beam, θ , is equal to the angle between the wavefront and the plane of the slits, it follows that sin θ = QY/QI where QP is the grating spacing (i.e. the centre-to-centre distance d between adjacent slits).

Fresnel Diffraction: A type of diffraction that occurs when wavefronts are partially obstructed, leading to complex interference patterns, often analyzed in near-field regions.