# The two mirrors illustrated in figure p35 15 meet at a right angle

### Chapter 37 : Interference of Light Waves

Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Determine the angles (a) 6 and (b) 0'. l Water l0, N! Figure P 9. (a) Show that if the mirror has rotated to make an angle 15 with the The reflecting surfaces of two intersecting flat mirrors are at an angle 0 (0°. The two mirrors illustrated in Figure P meet at a right angle. A laser beam is incident at an angle of ° from the vertical onto a. The two mirrors in Figure P meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 as shown. (a) Determine the distance the reflected.

If the experiment is repeated again with sheet 1 on top of sheet 3, what is the expected angle of refraction in sheet 3? Assume the same angle of incidence. When you look through a window, by how much time is the light you see delayed by having to go through glass instead of air?

Make an order-of-magnitude estimate on the basis of data you specify. By how many wavelengths is it delayed? Light passes from air into flint glass. Can the component of velocity parallel to the interface remain constant during refraction?

Because their speed changes, water waves refract when moving into a region of different depth. Sketch a map of an ocean beach on the eastern side of a landmass. Show contour lines of constant depth under water, assuming reasonably uniform slope. Demonstrate that the waves will move nearly perpendicular to the shoreline when they reach the beach. Again make a reasonable guess about the shape of contour lines of constant depth.

Suppose that waves approach the coast, carrying energy with uniform density along originally straight wavefronts. Show that the energy reaching the coast is concentrated at the headlands and has lower intensity in the bays. A prism that has an apex angle of What is its angle of minimum deviation? A triangular glass prism with apex angle Find the angle of deviation if the angle of incidence on the first surface is The apex angle of a prism is the angle between the surface at which light enters the prism and the second surface the light encounters.

A narrow white light beam is incident on a block of fused quartz at an angle of Find the angular width of the light beam inside the quartz. Light of wavelength nm is incident on the face of a fused quartz prism at an angle of The apex angle of the prism is Use the value of n from Figure The index of refraction for violet light in silica flint glass is 1. What is the angular dispersion of visible light passing through a prism of apex angle Consider a common mirage formed by super-heated air just above a roadway.

A truck driver whose eyes are 2. She perceives the illusion of a patch of water ahead on the road, where her line of sight makes an angle of 1. Find the index of refraction of the air just above the road surface. Treat this as a problem in total internal reflection. An optical fiber has index of refraction n and diameter d. It is surrounded by air. Light is sent into the fiber along its axis, as shown in Figure P Does the result for part a predict reasonable behavior as d approaches zero?

As n approaches 1? For nm light, calculate the critical angle for the following materials surrounded by air: Repeat Problem 36 when the materials are surrounded by water. Assume that the pipe has an index of refraction of 1.

When a penny diameter 1. However, when a dime diameter 1. What is the range of the possible depths of the air bubble beneath the surface? In aboutengineers at the Toro Company invented a gasoline gauge for small engines, diagrammed in Figure P The gauge has no moving parts. It consists of a flat slab of transparent plastic fitting vertically into a slot in the cap on the gas tank.

None of the plastic has a reflective coating. The plastic projects from the horizontal top down nearly to the bottom of the opaque tank. A lawnmower operator looks down from above and sees a boundary between bright and dark on the gauge.

The location of the boundary, across the width of the plastic, indicates the quantity of gasoline in the tank. Explain how the gauge works. Explain the design requirements, if any, for the index of refraction of the plastic. A swimmer gets into trouble The lifeguard takes negligible time to accelerate.

He can run at 7. To reach the swimmer as quickly as possible, in what direction should the lifeguard start running? You will need to solve a transcendental equation numerically. The flat photograph is in air, inside a vertical slot located behind a water-filled compartment having the shape of one half of a cylinder.

Suppose you are looking at the center of the photograph and then rotate the globe about a vertical axis. You find that the center of the photograph disappears when you rotate the globe beyond a certain maximum angle Fig.

Account for this phenomenon and calculate the maximum angle. Briefly describe what you would see when you turn the globe beyond this angle. Courtesy Edwin Lo Figure P A light ray enters the atmosphere of a planet where it descends vertically to the surface a distance h below. The index of refraction where the light enters the atmosphere is 1. A narrow beam of light is incident from air onto the surface of glass with index of refraction 1. Find the angle of incidence for which the corresponding angle of refraction is half the angle of incidence.

Draw a light ray incident from the air at angle of incidence Determine the angles of the reflected and refracted rays and show them on the diagram. Suppose instead that the light ray is incident from the glass at angle of incidence Determine the angles of the reflected and refracted rays and show all three rays on a new diagram. A small underwater pool light is 1.

The light emerging from the water forms a circle on the water surface. What is the diameter of this circle? One technique for measuring the angle of a prism is shown in Figure P A parallel beam of light is directed on the angle so that parts of the beam reflect from opposite sides. The light traverses 2. A young prisoner observes the patch of light moving across this western wall and for the first time forms his own understanding of the rotation of the Earth.

The mirror reflects light back to a spot on the eastern wall close beside the window. How fast does the smaller square of light move across that wall? The inner surfaces are plane mirrors.

A ray of light enters a small hole in the center of one mirror. The walls of a prison cell are perpendicular to the four cardinal compass directions. On the first day of spring, light Figure P When light is incident normally on the interface between two transparent optical media, the intensity of the reflected light is given by the expression Figure P A hiker stands on an isolated mountain peak near sunset and observes a rainbow caused by water droplets in the air 8.

The valley is 2. What fraction of the complete circular arc of the rainbow is visible to the hiker? The Sun is Take the index of refraction for water to be 1. A laser beam strikes one end of a slab of material, as shown in Figure P The index of refraction of the slab is 1. Determine the number of internal reflections of the beam before it emerges from the opposite end of the slab. Does it matter in part a whether the light is in the air or in the glass as it strikes the interface?

Refer to Problem 56 for its description of the reflected intensity of light normally incident on an interface between two transparent media. Treat this as a problem in total internal reflection. An optical fiber has index of refraction n and diameter d. It is surrounded by air. Light is sent into the fiber along its axis, as shown in Figure P Does the result for part a predict reasonable behavior as d approaches zero?

As n approaches 1? When a penny diameter 1. However, when a dime diameter 1. What is the range of the possible depths of the air bubble beneath the surface?

In aboutengineers at the Toro Company invented a gasoline gauge for small engines, diagrammed in Figure P The gauge has no moving parts. It consists of a flat slab of transparent plastic fitting vertically into a slot in the cap on the gas tank.

None of the plastic has a reflective coating. The plastic projects from the horizontal top down nearly to the bottom of the opaque tank. A lawnmower operator looks down from above and sees a boundary between bright and dark on the gauge. The location of the boundary, across the width of the plastic, indicates the quantity of gasoline in the tank. Explain how the gauge works. Explain the design requirements, if any, for the index of refraction of the plastic.

The shoreline of a lake runs east and west. A swimmer gets into trouble The lifeguard takes negligible time to accelerate.

He can run at 7. To reach the swimmer as quickly as possible, in what direction should the lifeguard start running? You will need to solve a transcendental equation numerically.

## Chapter 37 : Interference of Light Waves

The flat photograph is in air, inside a vertical slot located behind a water-filled compartment having the shape of one half of a cylinder. Suppose you are looking at the center of the photograph and then rotate the globe about a vertical axis.

You find that the center of the photograph disappears when you rotate the globe beyond a certain maximum angle Fig. Account for this phenomenon and calculate the maximum angle. Briefly describe what you would see when you turn the globe beyond this angle. Courtesy Edwin Lo Figure P A light ray enters the atmosphere of a planet where it descends vertically to the surface a distance h below. The index of refraction where the light enters the atmosphere is 1.

A narrow beam of light is incident from air onto the surface of glass with index of refraction 1. Find the angle of incidence for which the corresponding angle of refraction is half the angle of incidence.

Draw a light ray incident from the air at angle of incidence Determine the angles of the reflected and refracted rays and show them on the diagram. Suppose instead that the light ray is incident from the glass at angle of incidence Determine the angles of the reflected and refracted rays and show all three rays on a new diagram.

A small underwater pool light is 1. The light emerging from the water forms a circle on the water surface. What is the diameter of this circle? One technique for measuring the angle of a prism is shown in Figure P A parallel beam of light is directed on the angle so that parts of the beam reflect from opposite sides.

The walls of a prison cell are perpendicular to the four cardinal compass directions. On the first day of spring, light from the rising Sun enters a rectangular window in the eastern wall. The light traverses 2. A young prisoner observes the patch of light moving across this western wall and for the first time forms his own understanding of the rotation of the Earth. The mirror reflects light back to a spot on the eastern wall close beside the window. How fast does the smaller square of light move across that wall?

The inner surfaces are plane mirrors. A ray of light enters a small hole in the center of one mirror. When light is incident normally on the interface between two transparent optical media, the intensity of the reflected light is given by the expression Figure P A hiker stands on an isolated mountain peak near sunset and observes a rainbow caused by water droplets in the air 8.

The valley is 2. What fraction of the complete circular arc of the rainbow is visible to the hiker? The Sun is Take the index of refraction for water to be 1. A laser beam strikes one end of a slab of material, as shown in Figure P The index of refraction of the slab is 1.

Determine the number of internal reflections of the beam before it emerges from the opposite end of the slab.

## Section 35

Does it matter in part a whether the light is in the air or in the glass as it strikes the interface? Refer to Problem 56 for its description of the reflected intensity of light normally incident on an interface between two transparent media. Apply the transmission fraction in part a to find the approximate overall transmission through the slab of diamond, as a percentage. Ignore light reflected back and forth within the slab. This problem builds upon the results of Problems 56 and Light travels perpendicularly through a diamond slab, surrounded by air, with parallel surfaces of entry and exit.

The intensity of the transmitted light is what fraction of the incident intensity? Include the effects of light reflected back and forth inside the slab. The light beam in Figure P Find the speed of the spot of laser light on the wall. Assume the spinning mirror is at a perpendicular distance d from point O on a flat vertical wall. When the spot of laser light on the wall is at distance x from point O, what is its speed? Repeat the calculation for the case in which the polystyrene block is immersed in b water and c carbon disulfide.

Builders use a leveling instrument with the beam from a fixed helium—neon laser reflecting in a horizontal plane from a small flat mirror mounted on an accurately vertical rotating shaft. The light is Figure P Refer to Quick Quiz By how much does the duration of an optical day exceed that of a geometric day?

A shallow glass dish is 4.

When this dish is filled with water, the observer sees the center of the bottom of the dish. Find the height of the dish. A material having an index of refraction n is surrounded by a vacuum and is in the shape of a quarter circle of radius R Fig. A ray of light passes from air into water.

Derive the law of reflection Eq. A light ray traveling in air is incident on the left side of the cylinder. Determine the index of refraction of the material.

### Section 35_百度文库

Suppose that a luminous sphere of radius R1 such as the Sun is surrounded by a uniform atmosphere of radius R2 and index of refraction n.

When the sphere is viewed from a location far away in vacuum, what is its apparent radius? One face of a slab of thickness t is painted white, and a small hole scraped clear at point P serves as a source of diverging rays when the slab is illuminated from below. On the painted surface there appears a dark circle of diameter d, surrounded by an illuminated region, or halo. Is the inner edge of Figure P Students allow a narrow beam of laser light to strike a water surface.

They arrange to measure the angle of refraction for selected angles of incidence and record the data shown in the accompanying table. Use the resulting plot to deduce the index of refraction of water.

Angle of Incidence degrees Angle of Refraction degrees