Concept explainers
A dance hall is built without pillars and with a horizontal ceiling 7.20 m above the floor. A mirror is fastened flat against one section of the ceiling. Following an earthquake, the mirror is in place and unbroken. An engineer makes a quick check of whether the ceiling is sagging by directing a vertical beam of laser light up at the mirror and observing its reflection on the floor. (a) Show that if the mirror has rotated to make an angle ϕ with the horizontal, the normal to the mirror makes an angle ϕ with the vertical. (b) Show that the reflected laser light makes an angle 2ϕ with the vertical. (c) Assume the reflected laser light makes a spot on the floor 1.40 cm away from the point vertically below the laser. Find the angle ϕ.
Trending nowThis is a popular solution!
Chapter 34 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- The index of refraction for water is about 43. What happens as a beam of light travels from air into water? (a) Its speed increases to 43c, and its frequency decreases. (b) Its speed decreases to 34c, and its wavelength decreases by a factor of 34. (c) Its speed decreases to 34c, and its wavelength increases by a factor of 43. (d) Its speed and frequency remain the same. (e) Its speed decreases to 34c, and its frequency increases.arrow_forwardThe object in Figure P23.52 is mid-way between the lens and the mirror, which are separated by a distance d = 25.0 cm. The magnitude of the mirrors radius of curvature is 20.0 cm, and the lens has a focal length of 16.7 cm. (a) Considering only the light that leaves the object and travels first toward the mirror, locate the final image formed by this system. (b) Is the image real or virtual? (c) Is it upright or inverted? (d) What is the overall magnification of the image? Figure P23.52arrow_forwardLight travels from air into an optical fiber with an index of refraction of 1.44. (a) If the angle of incidence on the end of the fiber is 22 degree, what is the angle of refraction inside the fiber? (b) Light traveling through an optical fiber (n=1.44) reaches the end of the fiber and exits into air. (a) If the angle of incidence on the end of the fiber is 30 degree, what is the angle of refraction outside the fiber? (c) Calculate the critical angle of optical fiber and air interfacearrow_forward
- In Figure (a), a beam of light in material 1 is incident on a boundary at an angle of 28°. The extent to which the light is bent due to refraction depends, in part, on the index of refraction n2 of material 2. Figure (b) gives the angle of refraction 02 versus n2 for a range of possible n2 values, from na = 1.40 to np = 1.97. What is the speed of light in material 1? 38 28 28° 18° (a) (b) Number Units the tolerance is +/-5%arrow_forwardA spherical mirror is made by silver-coating half of the inside of a sphere of radius R = 20 cm. A light ray moves horizontally 5.0 cm above the axis of the mirror as in Fig.19.23. When reflected from the mirror, how far from the mirror does the ray cross the axis? You will need to use some trigonometry and geometry to solve this problem.arrow_forwardAn engineer is carrying out an experiment to determine the index of refraction for a partially reflective material. To do this, she aims a narrow beam of light at a sample of this material, which has a smooth surface. She then varies the angle of incidence. (The incident beam is traveling through air.) The light that gets reflected by the sample is completely polarized when the angle of incidence is 59.5°. (a)What index of refraction describes the material? n = (b)If some of the incident light (at ?i = 59.5°) enters the material and travels below the surface, what is the angle of refraction (in degrees)?arrow_forward
- The intensity of sunlight near the surface of the Earth is approximately 1.00 x 10³ W/m². What would be the side length (m) of a square mirror that would feel a 1.00 N force from sunlight when held so the plane of the mirror was perpendicular to the path of the light? 387 O 193 100 O 261 O 219 O 109 O 202 337 O 134 O 194arrow_forwardA laser beam has a velocity in a vacuum of c = 3 × 108 m/s. A student runs an experiment in which a liquid is placed in a tank of length L = 11.2 m. The time it takes for the beam to make it across the tank is timed to be t = 64 ns. (a) Write an expression for the liquid's index of refraction, n. (b) Numerically, what is this index?arrow_forwardThe critical angle for total internal reflection at a liquid-air interface is 42.5◦.at. If a ray of light traveling in the liquid has an angle of incidence at the interface of 35◦,what angle does the ray refracted in air make with the normal?b. If a ray of light traveling through air has an angle of incidence at the interfaces of 35◦, what angle does the ray refracted in the liquid make with the normal?arrow_forward
- A common trick in fiber optics is to send several colors of light down the same fiber (this is a form of what's called multiplexing). Each color of light can carry a separate signal, letting you squeeze more information into your beam. This, of course, leaves you with the problem of how to separate the colors back out once your beam gets to where its going. One way to do this involves total internal reflection.The index of refraction of glass isn't fixed; it's actually a function of frequency. Specifically, the index of the glass n and the angular frequency ω of the light are related by the equation below. Since different colors of light see different indices of refraction, different colors of light will see different critical angles.Suppose we have a beam with green light (frequency ω=3.7e+15 rad/s and red light (frequency ω=2.9e+15 rad/s traveling through this glass. Eventually, it's going to hit a glass-air boundary. At what angle of incidence θ should the light hit the boundary if…arrow_forwardA common trick in fiber optics is to send several colors of light down the same fiber (this is a form of what's called multiplexing). Each color of light can carry a separate signal, letting you squeeze more information into your beam. This, of course, leaves you with the problem of how to separate the colors back out once your beam gets to where its going. One way to do this involves total internal reflection.The index of refraction of glass isn't fixed; it's actually a function of frequency. Specifically, the index of the glass n and the angular frequency ω of the light are related by (see equation in image). Since different colors of light see different indices of refraction, different colors of light will see different critical angles.Suppose we have a beam with orange light (frequency ω=3.1e+15 rad/s and red light (frequency ω=2.9e+15 rad/s traveling through this glass. Eventually it's going to hit a glass-air boundary. At what angle of incidence θ should the light hit the…arrow_forward
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPrinciples 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
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning