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Two flat, rectangular mirrors, both perpendicular to a horizontal sheet of paper, are set edge to edge with their reflecting surfaces perpendicular to each other. (a) A light ray in the plane of the paper strikes one of the mirrors at an arbitrary angle of incidence θ1. Prove that the final direction of the ray, after reflection from both mirrors, is opposite its initial direction. (b) What If? Now assume the paper is replaced with a third flat mirror, touching edges with the other two and perpendicular to both, creating a comer-cube retroreflector (Fig. 34.8a). A ray of light is incident from any direction within the octant of space bounded by the reflecting surfaces. Argue that the ray will reflect once from each mirror and that its final direction will be opposite its original direction. The Apollo 11 astronauts placed a panel of corner-cube retroreflectors on the Moon. Analysis of timing data taken with it reveals that the radius of the Moon’s orbit is increasing at the rate of 3.8 cm/yr as it loses kinetic energy because of tidal friction.
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Chapter 34 Solutions
Physics for Scientists and Engineers
- A physicist directs a laser beam through a transparent medium, toward one surface of an equilateral prism. (The beam travels, and remains in, the plane of the page.) Incident on Surface 1 at an angle ?1, the beam then encounters Surface 2 from within the prism. If the angle of incidence at Surface 2 equals ?c , the critical angle for this prism, what is the original incidence angle, ?1 (in degrees)? The critical angle in this case is ?c = 40.5°. 40.5° 40.5° A prism in the shape of an equilateral triangle is shown. The triangle is upside down such that the base of the triangle is at the top of the figure and the apex is at the bottom. A laser beam comes in from the top left, moves down and to the right and is incident on the center of the base of the triangle. This surface is labeled Surface 1. The incident beam makes an angle of ?1 with the vertical. Within the prism, the beam continues to move down and to the right but at a slope which is steeper than the initial beam. It is incident…arrow_forwardA light ray travels from air (n=1.00) into a crown glass (n=1.52) with an angle of incidence of 49 degrees. The light ray continues to travel through the crown glass material into the diamond (n=2.42). At what angle does the light ray make with the normal line as it enters the diamond?arrow_forwardA block of crown glass is immersed in water as in the figure below. A light ray is incident on the top face at an angle of θ1= 41° with the normal and exits the block at point P. Find the angle of refraction θ2 of the light ray leaving the block at P. 80.2° 41° 43.3° 68.9°arrow_forward
- A block of crown glass is immersed in water as in the figure below. A light ray is incident on the top face at an angle of 38° with the normal and exits the block at point P. (a) Find the vertical distance y from the top of the block to P. 0.0642 m 0.0483 m 0.0353 m 0.0854 m (b) Find the angle of refraction θ2 of the light ray leaving the block at P.arrow_forwardFind the angle of incidence at which a light beam traveling from a medium having the index of refraction n1 = 2.7 to another medium having the index of refraction n2 = 1.4 suffers a total internal reflection.arrow_forwardAt what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524arrow_forward
- What is the measure of the incident angle for a light ray that bounces back on itself in a concave mirror? A. 0° B. 45° C. 90° D. 180°arrow_forwardA ray of light strikes the midpoint of one face of an equiangular (60°–60°–60°) glass prism (n = 1.5) at an angle of incidence of 31.4°. (a) Trace the path of the light ray through the glass, and find the angles of incidence and refraction at each surface.First surface: ?incidence = ° ?refraction = ° Second surface: ?incidence = ° ?refraction = ° (b) If a small fraction of light is also reflected at each surface, find the angles of reflection at the surfaces. ?reflection = ° (first surface) ?reflection = ° (second surface)arrow_forwardThe drawing shows a laser beam shining on a plane mirror that is perpendicular to the floor. The angle of incidence is 33.0°. The beam emerges from the laser at a point that is 1.10 m from the mirror and 1.80 m above the floor. After reflection, how far from the base of the mirror does the beam strike the floor?arrow_forward
- A ray of light strikes the midpoint of one face of an equiangular (60°–60°–60°) glass prism (n = 1.5) at an angle of incidence of 34.0°. (a) Trace the path of the light ray through the glass, and find the angles of incidence and refraction at each surface.First surface: ?incidence = ?refraction = Second surface: ?incidence = ?refraction = (b) If a small fraction of light is also reflected at each surface, find the angles of reflection at the surfaces. (first surface) ?reflection (second surface) ?reflectionarrow_forwardAn object is placed at x = 0 and a converging lens, with f1 = +25.0 cm, at x = 38.0 cm. A concave mirror, with f2 = +54.0 cm, is placed at x = 87.0 cm. Considering the light from the object that passes through the lens, reflects from the mirror, and passes through the lens again, find: (a) the x-coordinate of the final image;arrow_forwardA ray of light is reflected by two parallel mirrors (1) and (2) at points A and B. The ray makes an angle of 30° with the a parallel line between the two mirrors. Calculate for (a) the angle of reflection at the point of incidence A; (b) the angle of reflection at the point of incidence B (c) the apporxinatenumber of reflections made by the two mirrors if the distance between the two mirrors id d = 4 cm and the length L of the two mirror system is 3 meters, (d) In a real system, at each reflection, there are losses of the light energy travelling between the two mirrors. If L and d are fixed, what can be done to decrease the number of reflections on the mirrors and hence the energy lost by reflection?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning