Lecture 29

Summary

Young's interference
Dispersion
Diffraction

$diffraction grating wave fronts$

Quiz Bonus Ch.28

Diffraction

gratings (Many slit and
spectrometer applets)

Example #1

Example #2

$diffraction grating photo$

$diffraction grating diagram$

Holography
Video demonstration
Diffraction and interference

Example #3

Double-slit diffraction

$Double-slit diffraction geometry$

$Double-slit diffraction image$

$Double-slit diffraction pattern$

Two slit interference pattern, slits of width W separated by
distance d and illuminated by wavelength λ. What you see
is the Young's interference pattern modulated by the
single-slit diffraction pattern.

Lecture learning outcomes
A student who masters the topics in this lecture will be able to:

describe how diffraction gratings are able to separate colors of light into a spectrum that spans angles from 0° to 90° from the incident beam
use algebra to find the grating slit separation d, angle to a bright fringe θ_bright, order number m, or wavelength λ for a diffraction grating when any three of these quantities are given

Practice:
Try these additional examples

Example #4

Example #5

Prepare:
Read the textbook section on diffusion (on Canvas) before the next lecture

Walker5e 28.29
The oil film floating on water in the photo appears dark near the edges, where it is thinnest. The index of refraction of the oil is _____ than that of the water.

A. greater than
B. less than
C. the same as
D. impossible to say
Answer

gc6 tb24.34
Compare a 4000 lines/cm diffraction grating with a 6000 lines/cm grating.
A. The 4000 lines/cm grating produces greater dispersion.
B. The 6000 lines/cm grating produces greater dispersion.
C. The dispersions are equal but orders are sharper with 4000 lines/cm grating.
D. The dispersions are equal but orders are sharper with 6000 lines/cm grating.
Answer

gc6 24.33
Light falling normally on a 5695 line/cm grating produces a second-order bright line at 44.2°. What is the wavelength of the light?
$diffraction grating diagram$ A. 1985 nm
B. 1224 nm
C. 612 nm
D. 364 nm
Answer

Walker5e 28.40
An interferometric hologram has light and dark bands that are analogous to the interference fringes of an air wedge. If λ = 514 nm and 22 bright fringes are observed across an object, by how much did one end of the object flex with respect to the other?

A. 23.4 nm
B. 514 nm
C. 2.83 µm
D. 5.65 µm
Answer
wedge fringes and standing waves

Walker5e 28.Ex.17practice
If a diffraction grating is replaced by one that has more lines per centimeter, the angle to the second-order maximum will _____.
A. increase
B. decrease
C. stay the same
Answer

Walker5e 28.EYU.6
Suppose a diffraction grating has slits separated by 6 times the wavelength of light used to illuminate the grating. What is the angle corresponding to the m = 3 principal maximum?
A. 19.5°
B. 30.0°
C. 45.0°
D. 60.0°
Answer

A. greater than
There must be a phase change upon reflection at the top of the oil film but no phase change at the bottom of the oil film, so that the two reflected waves are nearly out of phase and interfere destructively.
thin film interference

B. The 6000 lines/cm grating produces greater dispersion.
The angular separation between wavelengths is proportional to the wavelength divided by the separation d between adjacent lines. Therefore the smaller d produces the larger dispersion.

C. 612 nm
solution equation

D. 5.65 µm
solution equation

A. increase
More lines per centimeter means a smaller slit separation d, which means a larger θ_bright for each principal maximum. The light passing through the new grating will be spread out over a larger range of angles.

B. 30.0°
solution equation

Notice that the m = 6 principal maximum occurs at an angle of sin⁻¹(1) = 90°, so there can be no maxima greater than m = 6.