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1. In a double-slit arrangement the slits are separated by a distance equal to 110 times the wavelength of the light passing through the slits.

**(a)** What is the angular separation between the central maximum and an adjacent maximum?

**(b)** What is the distance between these maxima on a screen 52.4 cm from the slits?

2. A double-slit arrangement produces interference fringes that have an angular separation of 3.32 x 10-3 rad for light with a wavelength of λ = 418 nm. For what wavelength would the angular separation be 9.93% greater?

3. Monochromatic light of wavelength 555 nm illuminates two parallel narrow slits 6.07 μm apart. Calculate the angular deviation of the third-order (for m = 3) bright fringe? Units

4. We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.27) so that reflection of light at wavelength 689 nm is eliminated by interference. What minimum thickness can the coating have to do this? (in nm)

5. A 660-nm-thick soap film (n = 1.43) in air is illuminated with white light in a direction perpendicular to the film. For how many different wavelengths in the 300 to 700 nm range is there

a. (a) fully constructive interference (__units)

b. (b) Fully destructive interference in the reflected light? (__units)

6. The rhinestones in costume jewelry are glass with index of refraction 1.50. To make them more reflective, they are often coated with a layer of silicon monoxide of index of refraction 2.00. What is the minimum coating thickness needed to ensure that light of wavelength 471 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference? ____nm

7. Monochromatic light of wavelength 577 nm is incident on a narrow slit. On a screen 1.51 m away, the distance between the second diffraction minimum and the central maximum is 1.73 cm.

a. **(a)** Calculate the angle of diffraction θ of the second minimum. (____units)

b. **(b)** Find the width of the slit in nanometers.(____units)

8. Light of wavelength 547 nm is incident on a narrow slit. The angle between the first diffraction minimum on one side of the central maximum and the first minimum on the other side is 1.34°. What is the width of the slit? (____units)

9. **(a)** How far from grains of red sand must you be to position yourself just at the limit of resolving the grains if your pupil diameter is 1.7 mm, the grains are spherical with radius 54 μm, and the light from the grains has wavelength 660 nm? ( _____units) **(b)** If the grains were blue and the light from them had wavelength 430 nm, would the answer to **(a)** be larger (show 1) or smaller (show 0)?

10. The radar system of a navy cruiser transmits at a wavelength of 1.5 cm, from a circular antenna with a diameter of 1.9 m. At a range of 8.3 km, what is the smallest distance in meters that two speedboats can be from each other and still be resolved as two separate objects by the radar system? (_____units)

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