CK-12-Physics - Intermediate

http://www.ck12.org Chapter 21. Physical Optics

come to the screen in the middle that has two small slits in it (hence the name Double-Slit Experiment). The light
waves then proceed like ripples out from the screen in the middle, until they reach the far side on the wall. Each
wave line can be thought of as the top of a ripple. The places where two ripples overlap is a point of constructive
interference. Two points of constructive interference are pointed out below.

FIGURE 21.5

What determines these points of constructive interference is the difference in path length from the slits.

• If the two paths are exactly the same distance, then the two waves will both be high and low at the same times,
  a case of constructive interference.


• If one path is exactly one-half of a wavelength shorter than the other, then the first will be high when the other
  is low and vice-versa, a case of destructive interference.


• If one path is a multiple of one wavelength, then the two waves will both be high and low at the same times, q
  case of constructive interference.

We can represent the wave fronts(W)using a ray diagram to determine the path difference between the waves
from each slit. Constructive and destructive interference occurs for path differences of whole wavelengths and path
differences of odd multiples of half-wavelengths, respectively. The result is a series of light (constructive) and dark
(destructive) fringes, as shown inFigure21.6.

TheFigure21.7 is used to determine an equation in terms of the wavelengthλ, the distancedbetween the double slit,
and the angle of diffractionθ.Figure21.8 shows an enlarged view of the two slits and the path difference,dsinθ.

Our assumption is that slit widthdis much less than the distanceL(dL)from the slits to the screen, and therefore,
the rays of light are nearly parallel, each making an angleθto the horizontal. Complementary angles show that the
angle^6 acbisθ.

Then sinθis equal to the ratio of the path difference(PD), shown in red inFigure21.8, to the distance between the
slitsd.

sinθ=PDd →PD=dsinθ

The path difference required for the constructive interference (bright fringes) can be expressed as

dsinθ=mλ,m= 0 , 1 , 2 ,...

For example, form=0, a bright fringe appears on the screen inFigure21.7 at pointA, since the path difference
between the two rays is zero. Rays from each slit to the screen at pointAare equidistant. We refer tomas the order
of the interference fringe. Form=0, it is order zero. These fringes are also called maxima or minima. A bright
fringe is called a maximum and a dark fringe is called a minimum.

And for destructive interference (dark fringes),

dsinθ=

(

m+^12

)

λ,m= 0 , 1 , 2 ,...

For the integer values ofm, the equation yields odd multiples of half-wavelength.