1. What is the speed of light in glass (n=1.43)? What is the wavelength of 589 nm light in that medium? Ans: 2.098 x 10⁸ m/s; 411.89 nm
2. Two slits separated by 0.80 mm create a first order line on a screen 50 cm away. The first order line is 0.304 mm from the central bright spot. What wavelength of light is seen? Ans: 486.4 nm
3. A grating with 4000 lines/cm is used to form a second order line at an angle of 34°. What is the wavelength of the light seen? Ans: 699 nm
4. A Young’s double slit experiment is performed using a slit separation of 0.2 cm and a slit-to-screen distance of 100 cm. How far from the central bright spot will the 1^st order line occur when 500 nm light is used? Ans; 0.00025 m
5. In a double slit experiment, 600 nm light is used to form the first order maximum at an angle of 3°. What is the slit separation? At what angle will the third order line occur? Ans: 1.15 x 10^-5 m; 9.03°
6. Light shines through a single slit whose width is 5.6 x 10^-4 m. A diffraction pattern is formed on a flat screen located 4 m away. The distance between the middle of the central bright spot and the first order dark bend is 3.4 mm. What is the wavelength of the light used? Ans: 4.7 x 10^-7 m
7. 5400 A light is used with a 2000 lines/cm grating to form a third order line. What is the angle? Is a tenth order line possible? Ans: 18.91°, no
8. When a grating is used with 575 nm light, a second order maximum is formed at an angle of 11.2°. How many lines per cm does this grating have? Ans: 1.689 x 10³ lines/cm
9. MgF₂ (n=1.38) coats a lens to reduce reflection from a glass (n=1.50) surface. How thick a coating is needed to produce minimum reflection for 550 nm (measured in a vacuum) light? Ans: 99.64 nm
10. The surface of a glass plate (n=1.50) is coated with a transparent thin film (n=1.25). A beam of 600 nm light traveling in air is incident on the film. The beam is partially transmitted and partially reflected. Calculate the frequency of the light. Calculate the wavelength of the light in the film. Calculate the minimum thickness of film such that the resulting intensity of light reflected back into the air is a minimum. Calculate the minimum nonzero thickness of film such that the resultant intensity of reflected light is a maximum. Ans: 5 x 10¹⁴ Hz; 480 nm; 120 nm; 240 nm
11. A thin gas (n=1.40) film floats on water (n-1.33). It appears yellow because blue light (469 nm in a vacuum) has been destructively interfered from the reflected light. Determine the minimum thickness of the film for this to occur. Repeat assuming that the gas film is floating on glass (n=1.52) rather than water. Ans: 167.5 nm; 83.75 nm
12. A soap bubble appears green (540 nm) at the point on its front surface nearest the viewer. What is its minimum thickness? Assume the soap bubble is water (n=1.33). Ans: 100 nm
13. A lens appears greenish yellow (570 nm) when white light reflects from it. What minimum thickness of coating (n=1.25) is used on such a glass lens (n=1.52)? Ans: 228 nm
14. An incident beam falls on the plane polished surface of a block of fused quartz, making an angle of 31.25° with the normal. This beam contains light of two wavelengths, 404.7 nm and 508.6 nm. The indices of refraction for quartz at these wavelengths are 1.4697 and 1.4619, respectively. The index of refraction of air may be assumed to be 1.0003 at both wavelengths. What is the angle between the two refracted rays? What is the speed of light of the two wavelengths in quartz? Ans: 0.1154°, 2.04 x 10⁸ m/s; 2.05 x 10⁸ m/s
15. A ray is incident normal to one face of a triangular prism of glass (in other words, it hits the prism face at an angle of 90° and continues through the prism without being refracted). At the opposite side of the prism, it hits the glass/air boundary at an angle of 45° relative to the normal, and is totally internally reflected. What is the index of refraction of glass? Ans: 1.41

Physical Optics Notes

Refraction Notes