Can someone please help me with the summary part and application part,

I have attached an example of what it should be as well as the notes.

Question:

A standard computer display has 96 pixels per inch. How close do you have to bring your eye to see the individual pixels? Assume the pupil has a diameter of 0.40 cm and the wavelength of light is 550 nm. (1 inch = 2.54 cm)

Answer:

1.6 m

Solution:

The minimum possible angular resolution is given by the Rayleigh's Criterion OR = 1.22 where d is the diameter of the pupil, and 1 is the wavelength of light. Using the small angle approximation the angular separation between the pixels from a distance of D is 0 ~ where y is the separation between the pixels. Then 1.22- 2/ 1 D lin . . 0.0254 m yd 96 lin. (0.40 . 10-2 m) D = = 1.6 m. 1.221 1.22 (550 . 10-9 m) Note that this is an idealized case, 20/20 vision is close to being diffraction limited but not quite. Most people will have to be a bit closer to make out individual pixels.Chapter 36 Summary and Resources X Robert Franz posted on Jul 31, 2023 1:22 PM Here is a summary of the main ideas in this chapter. 1. Diffraction is the spreading of waves after encountering an obstacle, corner, or slit comparable to the wavelength. For a slit of with 'a' an interference pattern of alternating max and min intensities will result. The location of the minimum can be described by the following equation: asin 0 = md m = 0, 1, 2, 3. . . where Ois the angle measured from the middle of the slit to the position on the screen as in chapter 35. 2. The intensity of a single slit diffraction pattern is given by I = Im(S a sina 2 where a = "a sin 0 and Im is 3. For a circular aperture, the location of the first minimum is given by the equation sin 0 = 1. 22 - where d is the diameter of the aperature. This defines Rayleigh criteria of resolvability defining the angle when two objects can be resolved from each other. For angles less than this, the objects will appear to blend together. 4. Waves passing through two slits produce a combination of a single and double slit interference pattern. The intensity as a function of angle can be described by I(0) = Im cos2 B ( sina ) 2 8 = "d sin 0; a = ! 5. A diffraction grating is a series of slits that can be used to separate a wave into its component wavelengths. The location of the diffraction maximum are given by the previous equation dsin 0 = md m = 0, 1, 2 . . . and the half-width of the diffraction maximum given by AOhw = Nd cos 0 where N is the number of slits and d is their spacing. 6. The dispersion (symbol D) of a diffraction grating is a measure of the angular separation of two lines differing it produces for wavelengths varying by 0. D = 40 m d cos 0 7. The resolving power (symbol R) of a diffraction grating is a measure of the diffraction gratings' ability to make emissions lines of closely spaced wavelength visible. R = Nave = Nm 8. X-ray diffraction occurs when x-rays are directed toward a solid with atoms spaced in a regular array of planes separated by spacing d. This is also known as Bragg Scattering. The maximum intensity pattern is formed at locations satisfying 2d sin 0 = ml