MCAT Physics and Math Review

Chapter 8: Light and Optics

8.3 Diffraction

Diffraction refers to the spreading out of light as it passes through a narrow opening or around an obstacle. Interference between diffracted light rays lead to characteristic fringes in slit–lens and double-slit systems. Diffraction and interference are significant evidence for the wave theory of light.

SINGLE SLIT

Although it is usually safe to assume that nonrefracted light travels in a straight line, there are situations where light will not actually travel in a straight-line path. When light passes through a narrow opening (an opening with a size that is on the order of light wavelengths), the light waves seem to spread out (diffract), as is shown in Figure 8.15. As the slit is narrowed, the light spreads out more.

Figure 8.15. Diffraction Light emerges from a narrow slit in a wide arc, not a narrow beam.

SLIT–LENS SYSTEM

If a lens is placed between a narrow slit and a screen, a pattern is observed consisting of a bright central fringe with alternating dark and bright fringes on each side, as shown in Figure 8.16. The central bright fringe (maximum) is twice as wide as the bright fringes on the sides, and as the slit becomes narrower, the central maximum becomes wider. The location of the dark fringes (minima) is given by the formula

a sin θ = nλ

Equation 8.13

where a is the width of the slit, θ is the angle between the line drawn from the center of the lens to the dark fringe and the axis of the lens, n is an integer indicating the number of the fringe, and λ is the wavelength of the incident wave. Note that bright fringes are halfway between dark fringes.

Figure 8.16. Single-Slit Diffraction with Lens

MULTIPLE SLITS

When waves interact with each other, the displacements of the waves add together in a process called interference, as described in Chapter 7 of MCAT Physics and Math Review. In his famous double-slit experiment, Thomas Young showed that the diffracted rays of light emerging from two parallel slits can interfere with one another. This was a landmark finding that contributed to understanding of light as a wave. Figure 8.17 shows the typical setup for Young’s double-slit experiment. When monochromatic light (light of only one wavelength) passes through the slits, an interference pattern is observed on a screen placed behind the slits. Regions of constructive interference between the two light waves appear as bright fringes (maxima) on the screen. Conversely, in regions where the light waves interfere destructively, dark fringes (minima) appear.

Figure 8.17. Young’s Double-Slit Experiment (a) Setup for experiment; (b) Interference pattern caused by a double-slit setup.

The positions of dark fringes (minima) on the screen can be found from the equation

Equation 8.14

where d is the distance between the two slits, θ is the angle between the line drawn from the midpoint between the two slits to the dark fringe and the normal, n is an integer indicating the number of the fringe, and λ is the wavelength of the incident wave. Note that bright fringes are halfway between dark fringes.

BRIDGE

Light is similar to other waveforms; it is affected by constructive and destructive interference when light passes through a slit and a lens, and when light passes through multiple slits. Interference also occurs with sound waves, as discussed in Chapter 7 of MCAT Physics and Math Review.

Example:

In a double-slit experiment, what is the linear distance y between the sixth and eighth minima on the screen? (Note: The wavelength λ is 550 nm, the slits are separated by a distance of 0.14 mm, and the screen is 70 cm from the slits.)

Solution:

The position of a dark fringe (minimum) is given by

We do not know the value of sin θ  However, for small angles, sin θ ≈ tan θ. This is because the length of the hypotenuse is very close to the length of the adjacent side. We do know the value of tan θ  so we can substitute it into the equation and still get very close to the correct answer:

Diffraction gratings consist of multiple slits arranged in patterns. Diffraction gratings can create colorful patterns similar to a prism as the different wavelengths interfere in characteristic patterns. For example, the organization of the grooves on a CD or DVD act like a diffraction grating, creating an iridescent rainbow pattern on the surface of the disc. Thin films may also cause interference patterns because light waves reflecting off the external surface of the film interfere with light waves reflecting off the internal surface of the film, as shown in Figure 8.18. Common examples of thin films are soap bubbles or oil puddles in wet parking lots. Note that the interference here is not between diffracted rays, but between reflected rays.

Figure 8.18. Thin Film Interference Interference patterns occur as light waves reflecting off the external surface of the film interfere with light waves reflecting off the internal surface of the film. Note that there would be a small degree of refraction as well, although this is not shown in the image.

X-RAY DIFFRACTION

X-ray diffraction uses the bending of light rays to create a model of molecules. X-ray diffraction is often combined with protein crystallography during protein analysis. Dark and light fringes do not take on a linear appearance, but rather a complex two dimensional image. An example of an x-ray diffraction pattern is shown in Figure 8.19.

Figure 8.19. X-Ray Diffraction Patterns

BRIDGE

X-ray diffraction and protein crystallography are commonly used to analyze the structure of proteins. These techniques, as well as a number of other protein assays, are discussed in Chapter 3 of MCAT Biochemistry Review.

MCAT Concept Check 8.3:

Before you move on, assess your understanding of the material with these questions.

1.    How does the diffraction pattern for a single slit differ from a slit with a thin lens?

·        Single slit:

·        Slit–lens system:

2.    What wave phenomenon do diffraction fringes result from?

3.    How does double-slit diffraction and interference differ from single-slit diffraction?

·        Double-slit:

·        Single-slit:

4.    True or False: Maxima in diffraction patterns are always equidistant between two minima.