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Essay on color, para. 2, reality in physics (continued)

Para. 2.5, dispersion (continued)

2.5.2 Dispersing Light with a Diffraction Grating
------------------------------------------------- In fig. 2.5-2, on the left side you see a double slit aperture, on the right side a screen.
Imagine that the distance   s   between aperture and screen were very much greater than the distance   a   between the slits. Further on, please imagine that from the left side a plane wave (i.e. a bundle of parallel rays) approaches the double slit.

Using the Huygens' principle, you can look at the two slits as being the origin for two new waves which propagate with concentric cylindrical wavefronts. Where the slits are the axes of the cylinders. Since we choose   a   to be very small, both cylindrical waves are coherent, i.e. synchronized to one another in frequency and phase.

Let us regard the screen center (point where screen and dashed axis intersect). To this point, both waves have to travel exactly equal path lengths. Both waves are in phase. Both wave components add their intensities to one another.

Now regard a point that has the distance   y   from the screen center.
Since   s>>a ,   we can assume the paths from both slits to this point as being parallel to one another.
Then the path lengths from both slits to this point differ by the amount   (delta) ,   which in turn depends on the angle   (Theta)   which is defined by the distance   y .

Increasing y continuously, once we will reach the situation where
(delta) = (lambda)/2 .
And this is the point where both waves have   180°   phase difference to one another. Here, total anihilation occurs. At this point and at this wavelength, total darkness is achieved.

These effects are called "diffraction" (changing direction) and "interference" (changing amplitude).
A different way of changing light direction is "refraction", which occurs at the interface of different media and which is used for example with the prism.

Using a new wavelength, there will be a new length   y   for total darkness, of course.

This way, white light impigning onto the double slit from the left is turned into stripes of consecutive colors on the screen.
Using very many slits at very dense spacing   a ,   you will achieve good color resolution and good light yield on the screen.

What I described
above, will -- strictly speaking -- only deliver color dependent directions of wide parallel bundles of light.
And indeed: If you make the grating illuminate a cylindrical lens and put the screen into the focal line of this lens, then you'll get a distinct increase in color definition and saturation.