Reeds Introductions: Physics Wave Concepts for Marine Engineering Applications (Reeds Professional) by Christopher Lavers

Author:Christopher Lavers [Lavers, Christopher]
Language: eng
Format: azw3
Publisher: Bloomsbury Publishing
Published: 2017-03-09T05:00:00+00:00

6.3 Diffraction at a slit

Considering figure 6.2, if the angle θ is such that the path difference OS-OP is then OS-OP waves will interfere destructively. Consequently, no light will be seen in the direction θ.

(eq 6. 1)

or since θ is very small, sin θ closely approximates to θ in radians.

6.4 Diffraction gratings

Diffraction gratings consist of many narrow, regularly spaced openings, and are produced in flat metallic coatings or with repetitive saw wave or sinusoidal surface profiles, essential for a wide variety of modern electro-optic components and functions. However, grating studies exist widely in nature as well and much research is currently underway to replicate the complicated structures of butterfly wings [6.2] and beetles [6.3] for optical applications as well as materials with structural light interference, such as cellulose. Butterflies such as the iridescent blue morpho butterfly (figure 6.5, see plate section) contain non-metallic gratings that give very strong reflections of blue light at precise angles of incidence.

Such gratings may in future provide interesting sensor elements as their behaviour changes dramatically if the environment varies near the grating. For example, if pure air (n = 1.0003) on the butterfly’s wing in the bottom right section is replaced with a thin coating of acetone (refractive index = 1.3590), the wavelength best reflected (brightest observed reflection) changes in a dramatic and startling manner from blue to green (figure 6.6, see plate section) [6.4].

Now, if parallel light falls on the grating, the result is that the wave front is split into many separate coherent sources. In some directions, the path differences between adjacent sources is λ and so the waves from all the sources across the grating will be in phase. In these directions, a bright image is formed. The condition for two adjacent sources to be in phase and for a bright spot on a screen is that d sinθ = n λ, where n is an integral number of wavelengths and d is the distance between regularly ruled openings in the diffraction grating; n also gives the order of the image (figure 6.7). White light splits into a number of spectra, since each colour exits the grating at a different angle (see figure 6.8, see plate section). The red wavelengths are diffracted and arrive at the screen in phase with a small value of θ displaced a short distance above (or below) the straight-through beam. The visible shorter violet wavelengths are displaced further in angle and vertical distance before again coming together in phase.

Note: The condition for a diffraction grating for constructive interference appears the same as that for a single slit, resulting in destructive interference. Remember the d here is the spacing between individual openings in the grating and does not refer to the slit width!

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