2: Laser eye surgery utilizes ultraviolet radiation with a wavelength around 185 nm. a) What is the frequency, in hertz, of the ultraviolet radiation? b) Assuming the precision, P, with which this electromagnetic radiation can shape the cornea is inversely proportional to wavelength (the shorter the wavelength, the higher the precision), how much more precise can this ultraviolet light be than the shortest wavelength of visible light, which is 380 nm? Give your answer in % more precise. Problem 3: On its highest power setting, a microwave oven can increase the temperature of 0.419kg of spaghetti by 45.0C in 120.s. a) Given that its specific heat is 3.76103J/(kgC), a value which is about 90% that of water, what was the rate of energy absorption, in watts, by the spaghetti? b) Find the average intensity of the microwaves absorbed by the spaghetti, in watts per squared meter, given that they are absorbed over a circular area 18.7cm in diameter. c) What is the peak electric field strength, in volts per meter, absorbed by the spaghetti? d) What is the corresponding peak magnetic field strength, in teslas? Problem 4: Suppose a man stands in front of a mirror. His eyes are 1.7 m above the floor, and the top of his head is 0.14 m higher. a) Find the height above the floor of the bottom of the smallest mirror in which he can see both the top of his head and his feet. (b) Find the height above the floor of the top of the smallest mirror in which he can see both the top of his head and his feet. Problem 5: A student stands do = 2.1 m in front of a floor-to-ceiling mirror. Her eyes are he = 1.43 m above the floor and she holds a flashlight at a distance hf = 0.95 m above the floor. Randomized Variables do = 2.1 m he = 1.43 m hf = 0.95 m Calculate the angle , in degrees, that the flashlight makes with respect to the floor if the light is reflected into her eyes. Problem 6: A student diver in a pool and an instructor on the edge, outside the water. Since the indices of refraction of air and water are different, the light rays coming from the diver and the instructor are refracted at the surface, changing their apparent position with respect to each other. The diver sees the instructor at an apparent angle of a = 21, measured from the normal to the interface. Randomized Variables a = 21 a) Find the height of the instructor's head above the water in meters, noting that you will first have to calculate the angle of incidence (you can take the indices of refraction to be na = 1 for air and nw = 1.33 for water). (b) Find the apparent depth of the diver's head below water as seen by the instructor in meters, assuming the diver and his image both have the same horizontal distance along the surface of the water. Problem 7: A fisherman spots a fish underneath the water. It appears that the fish is d0 = 0.63 m under the water surface at an angle of a = 42 degrees with respect to the normal to the surface of the water. The index of refraction of water is nw = 1.3 and the index of refraction of air is na = 1. a) The perpendicular distance from the apparent position of the fish to the normal of the water surface shown in the figure is L. Express L in terms of tan a and d0. b) Solve for the numerical value of L, in meters. c) Express the sine of the angle w, in terms of a, nw, and na. d) Solve for the numerical value of w in degrees. e) Now assume that the real position of the fish is directly below the apparent position, as shown in the figure. Express the real depth of the fish, d, in terms of L and tanw. show answer m f) Solve for the numerical value of d, in meters. Problem 8: An optical fiber uses flint glass surrounded by a crown glass cladding. a) What is the critical angle, in degrees, for total internal reflection? Problem 9: Suppose a pair of reading glasses found on the rack in a pharmacy has a power of 1.95 D. a) What is the focal length f, in centimeters? Problem 10: You note that your prescription for new eyeglasses is -4.5 D. a) What will their focal length, f, be in centimeters? Problem 11: A doctor examines a mole with a 15-cm focal length magnifying glass held 12 cm from the mole. Randomized Variables do = 12 cm a) What is the image distance for this configuration in meters? b) What is its magnification? c) How big is the image of a 5.00 mm diameter mole in millimeters? Problem 12: Suppose a book is held 5.3 cm from a 11.5-cm focal length lens. a) Find the magnification of the image of the book. b)Find the magnification of the lens when the book is held 9.8 cm from the magnifier. Problem 13: Consider a makeup mirror that produces a magnification of 1.55 when a person's face is 10.5 cm away. a) What is the focal length of the makeup mirror in meters? Problem 14: The print in many books averages 3.50 mm in height. Randomized Variables d0 = 34 cm a) How big (in mm) is the image of the print on the retina when the book is held 34 cm from the eye? Assume the distance from the lens to the retina is 2.00 cm. Problem 15: Suppose a certain person's visual acuity is such that he can see objects clearly that form an image 3.8 m high on his retina. Randomized Variables |do,max| = 3.8 m a) What is the maximum distance at which he can read the 75.0 cm high letters on the side of an airplane in km? Assume the image is formed on his retina, 2.00 cm behind the lens in his eye. Problem 16: A laser vision correction reshaping the cornea of a myopic patient reduces the power of his eye by 7.5 D, with a 5.0% uncertainty in the final correction. Randomized Variables P = 7.5 D What is the range of diopters of the spectacle lens that this person might have need after the LASIK procedure? Problem 17: A severely myopic patient has a far point of 2.5 cm. Randomized Variables do = 2.5 cm a) By how many diopters should the power of his eye be reduced in laser vision correction to obtain normal distant vision for him? Take 2.00 cm as the focal length of a normal relaxed eye lens (and also the distance of the retina from the lens) - that means a power of 50 D. Problem 18: A mother sees that her child's contact lens prescription is 2.25 D. a)What is the child's near point, in centimeters? Assume the near point for normal human vision is 25.0 cm. Problem 19: A simple compound microscope with an overall magnification of -950 has an objective that magnifies by -150. a) What is the magnification of the eyepiece? b) If there is another objective that can be used, having magnification of -400, what other total magnification is possible? Problem 20: You have a telescope with a 85 cm focal length objective. Recall that simple two-element telescopes invert the images of the objects viewed through them. Randomized Variables fo = 85 cm fe = 1.25 cm a) What is the angular magnification, M, of this telescope when equipped with a 1.25-cm focal-length eyepiece? PLEASE ANSWER ALL QUESTIONS THANK YOU