Will contain image distance after raytrace Will contain image height after raytrace

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1 Name: LASR 51 Final Exam May 29, 2002 Answer all questions. Module numbers are for guidance, some material is from class handouts. Exam ends at 8:20 pm. Ynu Raytracing The first questions refer to the optical system below and the ynu raytrace worksheet. You don t have to do a raytrace, but the questions assume that you are going to trace two rays. Ray a will be from the base of the object and will travel beginning with an angle of 0.1 radians to the optical axis. (tan(0.1)=0.1). It will terminate at the image location which will be the last surface in the system. Ray b will start at the tip of the object and travel initially parallel to the optical axis. 10 f=250 f=-250 The middle column of the table below the worksheet describes entries in the ynu worksheet. Some are numbers. Others are descriptions of numbers that will be calculated. In the right hand column of the table write the letter corresponding to the All dimensions in mm box of the ynu worksheet that the given information would be placed in. Note that zero gets placed in three boxes. Give those three answers in alphabetical order. -φ t y a f c a d b e j u a g y b h k u b i Will contain image distance after raytrace Will contain image height after raytrace LASR-51 Final Exam, page 1 of 6

2 Module What is the energy in wavenumbers of a photon of wavelength 500 nm? a) cm -1 b) 500 cm -1 c) cm -1 d) 1.2x10 4 cm When a beam of blue light in air with a wavelength of 400 nm enters a piece of glass with an index of refraction of 1.5. a) its speed decreases and its frequency increases. b) its speed decreases and its wavelength decreases. c) its frequency and wavelength both decrease. d) its speed increases and its frequency decreases. 14. The electric field in a light wave always oscillates: a) in the direction of propagation b) parallel to the magnetic field c) perpendicular to the direction of propagation. d) along a straight line e) all of the above 15. A Nd:YAG laser has a wavelength of 1.06 µm. What is its frequency? a) 2.83x10 10 Hz b) 9434 cm -1 c) 2.83x10 14 Hz d) 3.53x10 5 Hz 16. Which of the following describes Huygen's principle? a) Each point on a wavefront is considered to be a point source b) Two waves that arrive at the same point in phase interfere constructively c) Diffraction is important for apertures of the order of a wavelength d) Light travels slower in glass than in air e) Waves travel outward in concentric spheres from a point source 17. A laser beam with a diameter of 2 mm and a wavelength of 488 nm irradiates a circular aperture with a diameter of 0.3 mm. At a distance of 2 m from the aperture the size of the beam is found to be 8 mm. What is the Fresnel number that would be used to characterize the diffraction from the aperture after propagation of 2 m? a) 3.22 b) c) 51.5 d) 7.2x10-5 LASR-51 Final Exam, page 2 of 6

3 Module What thickness of a film of index 1.4 must be applied to a piece of glass of index 1.5 in order to make an antireflection coating for a wavelength of 500 nm? a) 125 nm b) 83 nm c) 89 nm d) 250 nm 19. The interference pattern from a double slit with a spacing of l=0.04 cm is observed on a screen 200 cm from the slits. It is found that the spacing between the fringes is 0.25 cm. What is the wavelength of the light? a) 500 nm b) 5x10-5 nm c) 1.667x10-5 cm d) 5 mm 20. The fringes shown in the diagram are observed on a shear-plate interferometer inserted into the output from a beam-expanding telescope. Which of the following can you conclude from this? a) The telescope output is not collimated. b) The laser resonator is misaligned. c) One of the lenses in the beam expander is defective. d) None of the above. 21. A HeNe laser with a wavelength of 633 nm illuminates a double slit. On a screen at some distance in the far field fringes with a spacing between bright fringes of 5.85 mm are observed. The HeNe laser is replaced by a different laser. The fringe spacing is now found to be 5.02 mm. The wavelength of the second laser is: a) 543 nm b) 738 nm c) 1064 nm d) There is not enough information to solve the problem. Module A HeCd laser with a wavelength of 442 nm illuminates a diffraction grating with 1200 l/mm at normal incidence. At what angle is the first order diffraction found? a) b) 21.6 c) 32.0 d) 3.68x10-7 LASR-51 Final Exam, page 3 of 6

4 23. Laser light is filling and passing through a 1 cm aperture. The light falls on a card placed 50 cm past the aperture. The light beam observed on the card has roughly the same shape as the aperture and has fairly uniform intensity except near the edges of the aperture where a number of fringes are observed. This is: a) Fresnel diffraction b) Fraunhofer diffraction c) completely explained by geometrical optics. d) an optical illusion caused by saturation of the eye by laser light. 24. The far field diffraction pattern of an aperture is being observed. If the aperture is made smaller, the diffraction pattern: a) gets smaller b) gets brighter c) gets larger d) can get larger or smaller depending on the wavelength 25. An excimer laser with a wavelength of 193 nm and a lens with an f/#=1.2 is used to image a mask onto a silicon wafer. According to the Rayleigh criterion what is the minimum separation distance that can be resolved by this system. (See fig. 14 module 5-7) a) 193 nm b) 232 nm c) 283 nm d) 566 nm 26. A rectangular aperture 0.5mm high and 2.0 mm wide is placed in front of a positive lens of focal length 1000 mm. A diffraction pattern is observed at the focal point of a lens. The wavelength is 500 nm. What is the size (full width) of the diffraction pattern? a) The diffraction pattern is 2 mm high and 0.5 mm wide b) The diffraction pattern is 0.25 mm high and 1 mm wide c) The diffraction pattern is 1.2mm high and mm wide d) The diffraction pattern is 1.0 mm high and 0.25 mm wide e) Cannot tell because 1000 mm is not large enough to be in the far field Module Light from an incandescent light is: a) linearly polarized b) circularly polarized c) unpolarized d) partially polarized LASR-51 Final Exam, page 4 of 6

5 28. Light from the sky directly overhead at sunset: a) linearly polarized b) circularly polarized c) unpolarized d) partially polarized 29. Light reflected from a glass plate at Brewster's angle is: a) linearly polarized b) circularly polarized c) unpolarized d) partially polarized 30. An example of a device that uses dichroic absorption to produce linearly polarized light is: a) Nicol prism b) Sheet polaroid c) Glan-Thompson polarizer d) Pile of Brewster plates 31. Light is passed through a horizontal linear polarizer. After passing through the horizontal polarizer the intensity is measured as 100 mw. The light is then passed through an ideal linear polarizer with its axis at 45 to the horizontal. Which of the following is true? a) The transmitted intensity is 50 mw and the beam is linearly polarized along the horizontal axis. b) No light is transmitted. c) The transmitted intensity is 50 mw and the beam is linearly polarized at 45 to the horizontal axis. d) The transmitted intensity is 100 mw and the beam is circularly polarized. 32. A birefringent crystal has an index of refraction that: a) depends on polarization b) depends on direction of propagation c) is larger than 2.1 d) both a and b 33. A quarter wave plate can convert linearly polarized light to circularly polarized light. What direction must the light be linearly polarized for this to occur? a) along the fast axis b) along the slow axis c) at 45 to the fast axis d) doesn't matter, a quarter wave plate always converts linear polarization to circular polarization LASR-51 Final Exam, page 5 of 6

6 34. If a linear polarizer is rotated in a beam of light and it is found that the intensity does not change with angle what can you say about the state of polarization of the beam. a) only that it is not linearly polarized, it can be circular, elliptical, or unpolarized b) it is unpolarized c) it is either unpolarized or circularly polarized d) it is either unpolarized, circularly polarized, or a mixture of the two. On this last problem make sure to use the corrected formulas given in class. Otherwise you will not get the correct answer. 35. A quarter-wave plate for a Nd:YAG laser is to be made from quartz. At the 1.06 µm wavelength of this laser, the refractive indices for quartz are n O = and n E = How thick should the plate be? a) 30.1 µm b) µm c) µm d) µm LASR-51 Final Exam, page 6 of 6