Question

What is the result of increasing the number of slits on the resulting diffraction pattern? What is a diffraction grating? What are they used for? Assuming you have light incident on a diffraction grating, at what angle do you except the second-order diffraction maximum to appear?

Answer 1

The diffraction pattern becomes spread out when the slit becomes narrower. (Correction: A single slit is not a "grating", just a single slit. A grating is a series of slits, many slits.)

Here is why: The angle for the the first minimum is given by
w sin (?min) = ?
where
? is the wavelength of the light,
?min is the angle between the central point and the first minimum,
the perpendicular is the line perpendicular to the slit and running to your eyes, or the display screen,
and w is the width lof the slit.

Since wavelength is constant, as the width w decreases, ?min must increase, which cause the location of the first minimum to move farther our from the central point, which causes the diffraction pattern to spread out.

Answer for Double Slit - Other Way Around (Diffraction pattern spreads out)

Here is why: Each band of light in the diffraction pattern is caused by constructive interference. Constructive interference occurs when
n? / d = x / L
where
? is the wavelength of the light,
d is the separation of the slits
n is the order of maximum observed (central maximum is n = 0),
x is the distance between the bands of light and the central maximum (also called fringe distance), and
L is the perpendicular distance from the slits to the screen (or retina of your eye).

Choose a given band of light to observe. It has some definite value for n. Now decrease separation d. Since n, ?, and L are constant, x must increase, where x is the distance from the central maximum to the band we are observing. (The central band is the band of light directly under the two slits, the band located on the screen directly across from the center of the two slits.) Hence the diffraction pattern spreads out.

Note: The intensity (brightness) of the band decreases, also.

Note: You are "looking through" the slit, so the bands of the diffraction pattern are displayed on the retina of your eye. Another way to view diffraction patterns is to let the diffracted light fall onto a screen, and view the screen with your eye. The equations apply to both cases, but can be more easily interpreted using the screen, because then the central point, the central maximum, the screen distance L, and the fringe distance x (from central maximum band to some fringe band), and ?min are easier to see