Lecture 41

Summary

Thin film interference
Single-slit diffraction
Circular apertures

$Double-slit diffraction geometry$

Double-slit diffraction

$Double-slit diffraction pattern$

$Double-slit diffraction image$

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

$diffraction grating$

$Diffraction grating$

Diffraction gratings

interactive applet
demos
formula

Example #1

Example #2

$diffraction grating diagram$

Diffraction and holography

Video demonstration

Example #3

Written Quiz Chs. 36-37

Practice:
Try these additional examples

Example #4

Example #5

Example #6

Prepare:
That's it! That's the last of the topics we'll learn this semester.

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

PSE6 38.27
A first order spectral line appears at 13.71° for a grating with 3660 lines/cm. What is its wavelength?
A. 867 nm
B. 315 nm
C. 422 nm
D. 648 nm
Answer

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.

D. 648 nm