Chapter 22

The angle of incidence of a light ray on a mirrored surface is \(30^{\circ} .\) What is the angle between the incident and reflected rays?

A beam of light is incident on a plane mirror at an angle of \(25^{\circ}\) relative to the normal. What is the angle between the reflected ray and the surface of the mirror?

A beam of light is incident on a plane mirror at an angle \(\alpha\) relative to the surface of the mirror. (a) Will the angle between the reflected ray and the normal be (1) \(\alpha\), (2) \(90^{\circ}-\alpha,\) or (3) \(2 \alpha ?\) (b) If \(\alpha=33^{\circ},\) what is the angle between the reflected ray and the normal?

Two upright plane mirrors touch along one edge, where their planes make an angle of \(\alpha\). A beam of light is directed onto one of the mirrors at an angle of incidence of \(\beta(\beta<\alpha)\) and is reflected onto the other mirror. (a) Will the angle of reflection of the beam from the second mirror be \((1) \alpha,(2) \beta,(3) \alpha+\beta,\) or \((4) \alpha-\beta ?\) (b) If \(\alpha=60^{\circ}\) and \(\beta=40^{\circ},\) what will be the angle of reflection of the beam from the second mirror?

Two identical plane mirrors of width \(w\) are placed a distance \(d\) apart with their mirrored surfaces parallel and facing each other. (a) A beam of light is incident at one end of one mirror so that the light just strikes the far end of the other mirror after reflection. Will the angle of incidence be (1) \(\sin ^{-1}(w / d),\) (2) \(\cos ^{-1}(w / d),\) or (3) \(\tan ^{-1}(w / d) ?(\mathrm{~b})\) If \(d=50 \mathrm{~cm}\) and \(w=25 \mathrm{~cm},\) what is the angle of incidence?

A beam of light is incident on a plane mirror at an angle of incidence of \(35^{\circ} .\) If the mirror rotates through a small angle of \(\theta\), through what angle will the reflected ray rotate?

The index of refraction in a certain precious transparent stone is \(2.35 .\) What is the speed of light in that stone?

The speed of light in the core of the crystalline lens in a human eye is \(2.13 \times 10^{8} \mathrm{~m} / \mathrm{s}\). What is the index of refraction of the core?

A beam of light traveling in air is incident on a transparent plastic material at an angle of incidence of \(50^{\circ} .\) The angle of refraction is \(35^{\circ} .\) What is the index of refraction of the plastic?

The critical angle for a certain type of glass in air is \(41.8^{\circ} .\) What is the index of refraction of the glass?

A beam of light in air is incident on the surface of a slab of fused quartz. Part of the beam is transmitted into the quartz at an angle of refraction of \(30^{\circ}\) relative to a normal to the surface, and part is reflected. What is the angle of reflection?

The laser used in cornea surgery to treat corneal disease is the excimer laser, which emits ultraviolet light at a wavelength of \(193 \mathrm{nm}\) in air. The index of refraction of the cornea is \(1.376 .\) What are the wavelength and frequency of the light in the cornea?

Light passes from material A, which has an index of refraction of \(\frac{4}{3},\) into material \(\mathrm{B}\), which has an index of refraction of \(\frac{5}{4}\). (a) The speed of light in material A is (1) greater than, (2) the same as, (3) less than the speed of light in material B. Explain. (b) Find the ratio of the speed of light in material A to the speed of light in material B.

The critical angle between two materials is \(43^{\circ} .\) If the angle of incidence is \(35^{\circ},\) what is the angle of refraction? (Consider that light can travel to the interface from either material.)

To a submerged diver looking upward through the water, the altitude of the Sun (the angle between the Sun and the horizon) appears to be \(45^{\circ} .\) (a) The actual altitude of the Sun is (1) greater than, (2) the same as, (3) less than \(45^{\circ} .\) Explain. (b) What is the Sun's actual altitude?

A submerged diver shines a light toward the surface of a body of water at angles of incidence of \(40^{\circ}\) and \(50^{\circ}\). Can a person on the shore see a beam of light emerging from the surface in either case? Justify your answer mathematically.

Light in air is incident on a transparent material. It is found that the angle of reflection is twice the angle of refraction. What is the range of the index of refraction of the material?

A coin lies on the bottom of a pool under \(1.5 \mathrm{~m}\) of water and \(0.90 \mathrm{~m}\) from the side wall ( \(\mathbf{F}\) Fig. 22.28 ). If a light beam is incident on the water surface at the wall, at what angle \(\theta\) relative to the wall must the beam be directed so that it will illuminate the coin?

A light beam traveling upward in a plastic material with an index of refraction of 1.60 is incident on an upper horizontal air interface. (a) At certain angles of incidence, the light is not transmitted into air. The cause of this is (1) reflection, (2) refraction, (3) total internal reflection. Explain. (b) If the angle of incidence is \(45^{\circ},\) is some of the beam transmitted into air? (c) Suppose the upper surface of the plastic material is covered with a layer of liquid with an index of refraction of \(1.20 .\) What happens in this case?

\(\mathrm{A} 15-\mathrm{cm}\) -deep opaque container is empty except for a single coin resting on its bottom surface. When looking into the container at a viewing angle of \(50^{\circ}\) relative to the vertical side of the container, you see nothing on the bottom. When the container is filled with water, you see the coin (from the same viewing angle) on the bottom of, and just beyond, the side of the container. (See Fig. \(22.24 .)\) How far is the coin from the side of the container?

An outdoor circular fish pond has a diameter of \(4.00 \mathrm{~m}\) and a uniform full depth of \(1.50 \mathrm{~m}\). A fish halfway down in the pond and \(0.50 \mathrm{~m}\) from the near side can just see the full height of a 1.80 -m-tall person. How far away from the edge of the pond is the person?

White light is incident from air onto a transparent material at an angle of incidence of \(40^{\circ} .\) The angles of refraction for the red and blue colors are \(28.15^{\circ}\) and \(27.95^{\circ},\) respectively. What are the indices of refraction for the two colors?

The index of refraction of crown glass is 1.515 for red light and 1.523 for blue light. (a) If light of both colors is incident on crown glass from air, the blue color will be refracted (1) more, (2) less, or (3) the same amount as the red color. Explain. (b) Find the angle separating rays of the two colors in a piece of crown glass if their angle of incidence is \(37^{\circ}\).

A beam of light with red and blue components of wavelengths \(670 \mathrm{nm}\) and \(425 \mathrm{nm}\), respectively, strikes a slab of fused quartz at an incident angle of \(30^{\circ} .\) On refraction, the different components are separated by an angle of 0.00131 rad. If the index of refraction of the red light is \(1.4925,\) what is the index of refraction of the blue light?

The angle of incidence and angle of refraction along a particular interface between two media are \(30^{\circ}\) and \(40^{\circ}\), respectively. What is the critical angle for the same interface?

Light passes from medium A into medium \(B\) at an angle of incidence of \(30^{\circ} .\) The index of refraction of A is 1.5 times that of B. (a) What is the angle of refraction? (b) What is the ratio of the speed of light in \(\mathrm{B}\) to the speed of light in \(\mathrm{A} ?\) (c) What is the ratio of the frequency of light in \(B\) to the frequency of light in A? (d) At what angle of incidence would the light be internally reflected?

An optic fiber of index of refraction of 1.6 is surrounded by a layer called the cladding layer. The index of refraction of the cladding is \(1.3 .\) If the angle of incidence inside the fiber is \(40^{\circ},\) will there be light leaking into air? What if the angle of incidence is \(50^{\circ} ?\)