he figure shows light of wavelength λ incident at angle φ on a reflection grating of spacing d. We want to find the angles θm at which constructive interference occurs. a. The figure shows paths 1 and 2 along which two waves travel and interfere. Find an expression for the path-length difference ∆r = r2 − r1. b. Show that the zeroth-order diffraction is simply a “reflection.” That is θo = φ. c. Light of wavelength 500 nm is incident at φ = 40o on a reflection grating having 700 reflection lines/mm. Find all angles θm at which light is diffracted. Negative values of θm are interpreted as an angle left of the vertical. d. Draw a picture showing a single 500 nm light ray incident at θm = 40o and showing all the diffracted waves at the correct angles.

A laser beam (λ=513 nm) is put through a beam splitter to give 2 equal intensity beams traveling parallel to one another. One of these beams is directed through a double slit apparatus, and the other beam through a single slit apparatus. The single slit and the double slits are in the same plane and both display fringe patterns on a screen a distance L= 4.4 m away. a. The slit spacing of the double slit apparatus is 0.52 mm. What is the distance from the center of the double slit fringe pattern to the 5th dark fringe? b. If the third dark fringe of the single slit pattern is the same distance from the center of the single slit pattern as the result for part (a), what is the single slit width?   To continue, please enter the result of part b) in mm.   Round your answer to 2 decimal places.

A film material with n coating is 380nm thick. White light is incident perpendicularly to the coating. a. Calculate the frequency of a green light (570TH2) inside the film. 1.25 is used as a coating on a piece of flat glass (n : 1.55). The

A laser beam (λ=497 nm) is put through a beam splitter to give 2 equal intensity beams traveling parallel to one another. One of these beams is directed through a double slit apparatus, and the other beam through a single slit apparatus. The single slit and the double slits are in the same plane and both display fringe patterns on a screen a distance L= 3.3 m away. a. The slit spacing of the double slit apparatus is 0.63 mm. What is the distance from the center of the double slit fringe pattern to the 5th dark fringe? b. If the third dark fringe of the single slit pattern is the same distance from the center of the single slit pattern as the result for part (a), what is the single slit width?   To continue, please enter the result of part b) in mm.   Round your answer to 2 decimal places

reflective diffraction grating is to have a grating spacing of 3 microns. a. If you want the 2nd order 450 nm to be retroreflected (Littrow mount), what is the blaze angle? b. What is the angle between the 450 nm 2nd order and 451 nm 2nd order reflections?

An oil film (n = 1.46) floats on a water puddle. You notice that green light (X= 528 nm) is absent in the reflection. Part A What is the minimum thickness of the oil film? Express your answer to three significant figures. V ΑΣΦ Sw ? nm

Question A2 Red light of vacuum wavelength 650 nm is travelling in a non-magnetic dielectric glass of refrac- tive index ng = 1.60. Calculate the impedance of the glass, the wavelength of light in the glass, and the critical angle 0c for total internal reflection at a glass-air interface. Question A3 Light is incident from air onto a horizontal surface of water of refractive index nw = 1.33. Calculate the Brewster angle at which the reflectance for the TM polarisation is zero. Also, cal- culate the power reflection coefficient RTE for TE-polarised light incident at this Brewster angle.

A flat screen is located 0.67 m away from a single slit. Light with a wavelength of 510 nm (in vacuum) shines through the slit and produces a diffraction pattern. The width of the central bright fringe on the screen is 0.051 m. What is the width of the slit? Number i Units

We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.32) so that reflection of light at wavelength 563 nm is eliminated by interference. What minimum thickness can the coating have to do this? Number i 93.8 Units nm

The figure shows four different cases where light of wavelength A reflects from both the top and the bottom of a thin film of thickness d. The indices of refraction of the film and the media above and below it are indicated in the figure(Figure 1). Figure 1.6 1 1.5 1.4 1.4 1.5 1.6 1.5 1.6 1.4 2 3 1 of 1 4 1.4 1.6 1.5 Y Part A For which of the cases will the two reflected rays undergo constructive interference if d=X/4? constructive interference occurs in case 2 and case 3 O constructive interference occurs in case 2 and case 4 constructive interference occurs in case 3 and case 4 constructive interference occurs in case 1 and case 2 Submit Part B Request Answer For which of the cases will the two reflected rays undergo constructive interference if d=λ/2? O constructive interference occurs in case 2 and case 3 O constructive interference occurs in case 2 and case 4 O constructive interference occurs in case 3 and case 4 constructive interference occurs in case 1 and case 2