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Lecture 12: Diffraction and Diffraction Gratings
March 4, 2025
Reading Assignment
- Read: 32.6; Supplementary Reading Ch 1.4-1.7
- Study: Figs 32.24, 32.26; Supp Exs 1-5, 1-6, 1-7
Objectives
- (Continuing objective) Describe applications of the concepts of induction, waves, and light to everyday “real life” situations.
- Use the method of phasors to locate maxima and minima in a two-slit interference problem, multi-slit interference pattern, or for diffraction gratings.
- Explain how diffraction gratings can be used to separate colors.
- Using phasors, determine the phase difference corresponding to successive minima in a single slit diffraction pattern. From this, find the angles and screen locations of minima and determine the width of the “bright” central maximum.
- Describe diffraction, and explain how diffraction limits resolution. Use Rayleigh's criterion to solve resolution problems.
Homework
- Wednesday's Assigned Problems:
A45, A46, X11 (below), X12 (below); CH 32: 25, 29, 31; Supp CH 1: 7, 9
Answers: X11 (a) 2, (b) 1
Problem X11 Light is normally incident on a grating with 10,000 lines/cm. (a) Find the maximum order in which 450 nm light will be visible, and (b) in which 650 nm light will be visible.
Problem X12 For visible light with wavelengths from 400 nm to 700 nm, show that the first-order spectrum is the only one that doesn't overlap with the next higher order.
- Monday's Hand-In Problems from Lecture 12:
A47, A105; CH 32: 18, 48; Supp CH 1: 8
Note: this is only the first half of the hand-in set.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 3,5; CT2 - 3; CT3 - 5; CT4 - 1
- Spreadsheet showing phasor diagrams for 3-, 4-, and 20-source interference.
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Example 1: Resolution limits.
- Example of three source interference.
- Example of single-slit diffraction problem.
Pre-Class Entertainment
- Baby Love - The Supremes
- Best of My Love - The Emotions
- Save Me - Aretha Franklin
- Got to Be Real - Cheryl Lynn
- I Will Survive - Gloria Gaynor
Assigned Problems Guide
- A45: medium. Exactly what we did in lecture for the CD, except now with a angle for the first order maximum.
- A46: quick experience problem. We'll bring a CD to problem session.
- X11: medium long. Why is there a maximum order (bright spot)? Because $\theta$ can't be bigger than $90^\circ$. Work back from that to find the maximum $\Delta\phi_\text{adj}$ and then interpret.
- X12: medium. First, find the general expression for the angle $\theta$ of the $n$th order bright spot in terms of $n$, $\lambda$, and $d$. Think about what it means for the spectra to overlap in terms of these angles.
- 32-25: medium. Find $\theta_\text{1st min}$ for a single-slit. Then double it (because it goes in both directions from the central max).
- 32-29: medium quick. “Angular diameter” means the angle $\theta$ between different parts of the object (like the two lines on the chalkboard). You'll need to convert it to radians.
- 32-31: Finding $\theta_\text{1st min}$ for the human eye.
- Supp 1-7: challenging. You'll need to find $r_1$, $r_2$, and $r_3$ for each radio tower. Then you will have two different $\Delta r$'s: $\Delta r_{12} = r_2-r_1$ and $\Delta r_{23} = r_3-r_2$. Convert those to $\Delta\phi$'s and try to make the phasor diagram.
- Supp 1-9: medium. How can I add up four phasors to get zero? What shape do I need? What is the associated $\Delta\phi_\text{adj}$?