Chapter 34, Problem 041 A lens is made of a transparent material having an index of refraction of 1.70. One side of the lens is flat, and the other convex with a radius of curvature of 27.0 cm. (a) Find the focal length of the lens. (b) If an object is placed 51.0 cm in front of the lens, where will the image be located? (a) Number Units (b) Number Units
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- (Dove Prism) A new type of prism inverts an image that comes in through one end (see Figure 1). The prism will be shaped like a trapezoid with a square cross-section and sides cut at a 45° angle, and that the prism will be made of a plastic called BK7 that has an index of refraction of 1.517. Decide on the dimensions of the prism in order to maximize the size of the image that can be inverted (see incoming/outgoing rays in the side view in Figure 2). How long (length B in Figure 1) should the prism be in terms of its height (length A in Figure 1)? What happens to an image that enters the prism on one side of its long face (see figure 3)? Make a drawing tracing the path of rays 4, 5, and 6 in figure 3 to find out. Figure 1 Figure 2 1 3 2 45° 3 1 Figure 2 Figure 3 45° Figure 3 4 5 6An optician is designing a contact lens. The material has is an index of refraction of 1.30. In order to yield the prescribed focal length, the optician specifies the following dimensions: inner radius of curvature = +2.46 cm outer radius of curvature = +2.02 cm where the inner radius of curvature describes the surface that touches the eye, and the outer radius of curvature describes the surface that first interacts with incoming light. What is the focal length of this contact lens (in cm)?The kitten, Simba (Fig. A) and the kitten, Bella (Fig. B) are inspecting a goldfish swimming inside a round aquarium filled with water (nwater = 1.33). The magnitude of the radius of the round surface of the aquarium is 16 cm. The kittens are in air (nair=1.00). In order to calculate the apparent depth of the fish as viewed by the kittens, you need to use the equation shown in Fig. C. Identify the following (Please note that I am not asking you to do the calculation) n₁ P Fig. A + n₂ 9 = (n₂-n₁) R Fig. C Fig. A: n₁ = Fig. B: n₁ = ; n₂ = _; n₂ = Fig. B ; R = ; R =
- One positive lens (focal length = f1) and one negative lens (focal length = -f2) are placed at a distance d. – All lenses are thin lenses. Find the overall ABCD matrix of the system Find the value of d when “C” of the overall matrix is zero. ( Hint : Find d in terms of f1 and f2) (This is when the focal length of the overall system is infinity.)A beam of light enters from air into a slab of glass (nglass=1.5) along a surface tilted at a 45 degree angle from the horizontal. What is the angle?Two plane mirrors make an angle α = 54.0◦ between them. A ray of light incident on one of the mirrors is reflected and hits the second mirror. Find the angle β between the ray incident on the first mirror and the ray reflected off of the second mirror. (a) 36.0◦ (b) 72.0◦ (c) 54.0◦ (d) 24.0◦ (e) None of the above.
- A spherical mirror is to be used to form an image, five times as tall as an object, on a screen positioned 5.8 m from the mirror. (a) Describe the type of mirror required. The mirror is a Mirror Type-mirror and it has a focal length of (b) Where should the mirror be positioned relative to the object? m. Submit Answer The object should be m in front of the mirror.Question 9 Suppose the isosceles prism of the figure has apex angle p enter the left face of the prism and exit the right face? (b) What angle of incidence e is required for the ray to exit the prism with an identical angle e for its refraction, as it does in the figure? 50.9° and index of refraction n = 1.52. (a) What is the smallest angle of incidence e for which a ray can (a) Number Units (degrees) (b) Number Units ° (degrees)Homework 12 Problem 4: A shopper standing 2.75 m from a convex security mirror sees his image with a magnification of 0.23. Part (a) What is his image distance in meters, measured from the surface of the mirror, given that the object distance is positive? di = ______ Part (b) What is the focal length of the mirror, in meters? f = ______ Part (c) What is its radius of curvature in meters? R = ______
- A plano-convex lens is one with a convex surface on one side and a flat surface on the other. Suppose a thin lens is made of glass with index of refraction 1.5. If the radius of curvature of the curved surface is 1.1 meters, what is the focal length of the lens? Give your answer in meters.cem 1 1 of 1 Use this information for parts G, H and I. The sideview mirror on your car is convex. When looking in this mirror, you see a car that has an actual distance of 100 m behind you (the distance from the car to the mirror) and the image appears to be only -1.961 m from the mirror. Part G What is the focal length of this mirror? Answer in units of m to four significant figures. Do not Include the units symbol. Submit Request Answer Part H If the image of the car appears to be 2.941×10¬2 m tall, what is the height of the actual car? Answer in units of m to four significant figures. Do not include the units symbol. ? Submit Request Answer Part I