 Phyllis Fleming Physics Physics 106
 Review - Geometric Optics
 1 In Fig. 1 below, label the angle of incidence Θi, the angle of reflection Θr, and the angle of refraction or transmission Θt. 2 As shown in Fig. 2 below, a light ray hits a surface normally. What is the angle of (a) incidence, (b) reflection, and (c) refraction? 3 For Fig. 3 below, find (a) the angle of reflection and (b) the angle of refraction. Redraw Fig. 3 and show the reflected and the refracted rays. The incident ray is in air with index of refraction ni = 1.00 and transmitted in a medium with index of refraction nt = 1.50. 4 Light from a point object O in Fig. 4 below hits the mirror MM’. Draw one incident ray from the object that hits the mirror normally and its reflected ray. Draw another incident ray with an angle of incidence of about 20o and its reflected ray. Since we think of light as coming from rays diverging from an object, it appears that the reflected light comes from a point behind the mirror. Dash the reflected rays behind the mirror until they meet and label this point I for image. Compare the distances of O and I from the mirror. 5 A light beam is incident upon a parallel glass plate, as shown in Fig. 5 below. Find the angle of (a) refraction at the first glass surface, (b) incidence at the lower glass-air surface, (c) refraction as the ray goes from glass to air. Use these angles to trace the path of the ray from air to glass and then from glass to air. 6 A beam of light of wavelength λ is incident from air upon the prism (n = 1.532) of Fig. 6 below at an angle of 50o. Find the angle of (a) refraction as the light enters the prism, (b) the angle of incidence at the other side of the prism, and (c) the angle of as the ray passes from glass to air. Use these angles to trace the path of the ray from air to glass and then from glass to air. (d) If light of wavelength λ’ > λ for which its index of refraction n’ is less than n, compare its path into and through the prism with that of the path for the light of wavelength  λ. 7 Light is incident from a medium ni at an angle of 48.6o as shown in Fig. 7 below. What is (a) the angle of refraction in air and (b) the index of refraction ni of the medium? (c) The angle of incidence is now increased to 60o. Using Snell's law and the ni you found in part (b), find the sine of the new angle of refraction. This is impossible. What happens? 8 As shown in Fig. 8 below, a light ray is incident normally on one face of a 30o-60o-90o dense flint (n = 1.655) prism that is immersed in water (n = 1.333). (a) Determine the exit angle Θ4 of the ray. (b) A substance is dissolved in the water to increase the index of refraction. At what value of n of the mixture will total internal reflection cease at point P? 9 A cylindrical tank with an open top has a diameter of 3.0 m and is completely filled with water. When the setting sun reaches an angle of 28o above the horizon, sunlight ceases to illuminate the bottom of the tank. How deep is the tank?
 10 A microscope is focused on a small scratch on the top surface of a glass slide. When a cover slip with a thickness of 500 µm is placed on the slide, the microscope must be raised by 120 µm to bring the scratch back into focus. What is the index of refraction of the cover slip? Assume that all rays entering the microscope make small angles with the normal to the slide so that sin Θ is approximately equal to tan Θ.
 11 A light ray is incident upon a semicircular container of water at an angle of 53o as shown in Fig.9 below. The index of refraction of water is 4/3. Trace the path of the ray through the water and out into the air, labeling angles of incidence and refraction. Ignore any refraction at the surface of the container. 12 A ray of light is incident normally on one face of a triangular prism of glass as shown in Fig. 10 below. The light is totally internally reflected inside the prism. (a) What is the minimum index of refraction of the prism that will cause all the light entering the prism to emerge as shown? (b) If the index of refraction is too small, some light will be refracted at the diagonal face. Which path (1, 2, or 3 of Fig. 10) will it follow? Explain your answer. 13 A thin converging lens has a focal length of 10 cm. Find by (i) calculation and (ii) construction of a ray diagram the position of the image of an object for the object distance so equal to (a) 30 cm, (b) 15 cm, and (c) 5.0 cm. Also find the magnification for each case. Describe whether the image is real or imaginary, erect or inverted, magnified or diminished.
 14 A thin diverging lens has a focal length of 10 cm. Find by (i) calculation and (ii) construction of a ray diagram the position of the image of an object for object distance equal to (a) 30 cm and (b) 4 cm. Also find the magnification for each case. Describe whether the image is real or imaginary, erect or inverted, magnified or diminished in size.
 15 An object 1.0 cm high is 100 cm from a converging lens. The inverted image is 3.0 cm high. Find the focal length of the lens.
 16 When a person holds a magnifying glass 8.0 cm away from an object that is 2.0 cm wide, she sees a virtual image of the object, which is 6.0 cm wide. What is the focal length of the magnifying glass?
 17 A projector forms an image of a 5.0 cm x 5.0 cm slide on a screen. If the image is 95.0 cm on a side and the distance from the slide to the screen is 4.00 m, what is the focal length of the projector's lens?
 18 When an object is placed 12 cm to the left of a lens, a virtual image is formed 6.0 cm from the lens on the same side as the object. What is the focal length of the lens? Is it a converging or a diverging lens?
 19 The objective and the eyepiece of a microscope each have a focal length of 2.0 cm. If an object is placed 2.2 cm from the objective, calculate (a) the distance between the lenses when the microscope is adjusted for minimum eyestrain and (b) the magnification of the microscope.
 20 A comet-seeker's telescope has an objective lens of focal length 40 cm and an eyepiece of power 30 diopters. What is the magnifying power of the microscope?
 21 Find by calculation and construction of ray diagrams the image of a concave mirror of focal length 10 cm when so is (a) 30 cm and (b) 5 cm. Find the magnification and classification of the image for both cases.
 22 Rays parallel to the principal axis of a converging lens and concave mirror pass through the lens and are reflected by the mirror, which is to the right of the lens. If the distance between the lens and mirror is (f1 + f2), where f1 and f2 are the focal lengths of the lens and mirror, respectively, locate the final image. The incident light is incident from the left of the lens.
 23 Fermat's principle states that a light ray that connects two points within a medium follows a path for which the transit time of the light is a minimum. The length traveled by the light L = ct for vacuum or air and L = vt = ct/n or t = nL/c for a medium of index refraction n. If light travels the shortest distance, it takes the minimum time. Use Fermat's principle to prove Snell's Law: n1 sin Θ1 = n2 sin Θ2. Refer to Fig. 11 below and find when dt/dx = d(n1L1/c + n2L2/c) = 0. 24 Two converging lenses, both of focal length 10 cm, are separated by 20 cm. An object is 15 cm to the left of the first lens. Find by calculation and construction of a ray diagram the position of the image. Find the magnification of the image and describe whether it is real or imaginary, erect or inverted, magnified or diminished.
 25 A double convex lens with equal curvature radii of 38-cm is made from glass with indices of refraction of 1.51 for red light and 1.54 for blue light. If a point source of white light is place on the lens axis at 95 cm from the lens, over what range will its visible image be smeared?
 26 A person has a far point at 4.0 m. Describe the lens that will correct this defect.
 27 A person has a near point at 1.25 m. Describe the lens that will correct this defect.

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