When coherent (all in phase), monochromatic (single color or frequency) light pa

Question

When coherent (all in phase), monochromatic (single color or frequency) light passes through a pair of slits, one observes a pattern of dark and bright bands on a screen. When you increase the number of slits, much more light makes it through the openings and the interference effects become much more pronounced. Thus you get a brighter set of spots and much sharper bright spots.
A diffraction grating has a lot of tiny parallel slits. The angle at which you find constructive interference can be determined using the same formula as with Young's Double Slit experiment. The one adjustment is that you need to convert the line density (number of lines per unit length) into the distance between adjacent slits (see the text).
Suppose you have a diffraction grating which has 300. lines/mm and you shine light with a wavelength of 419 nm through it.

a.) What is the angle at which you will observe the second order (m=2) bright fringe?

b.) If the screen is 3.20 m away from the diffraction grating, what is the distance on the screen between the bright central and the second order bright fringe?

Explanation / Answer

N = 300 lines/mm

N = 1/d = 300000 lines/m

lamda = 419 nm

d*sin(theta) = m*lamda

theta = arcsin(m*lamda/d)

(a) m= 2

theta = arcsin(2*419*10^-9*300000)

theta = 14.56 degrees

(b) D = 3.2 m

Y = m*lamda*D/d

Y = 2*419*10^-9*3.2*300000

Y = 0.805 m

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