33. Geometric Optics

(I) The speed of light in ice is 2.29 x 10⁸ m/s. What is the index of refraction of ice?

A 50-year-old man uses +2.5 D lenses to read a newspaper 25 cm away. Ten years later, he must hold the paper 32 cm away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 cm away? (Distances are measured from the lens.)

The critical angle for a certain liquid–air surface is 52.6°. What is the index of refraction of the liquid?

A light beam strikes a piece of glass at a 55.00° incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively. What is the angle between the two refracted beams?

(II) A beam of light is emitted in a pool of water from a depth of 65.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit the water?

A beam of light is emitted 7.7 cm beneath the surface of a liquid and strikes the surface 7.2 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid?

A light beam strikes a 2.5-cm-thick piece of plastic with a refractive index of 1.62 at a 45° angle. The plastic is on top of a 3.8-cm-thick piece of glass for which n = 1.47. What is the distance D in Fig. 32–51?

(II) A 13.0-cm-thick plane piece of glass (n = 1.54) lies on the surface of a 12.0-cm-deep pool of water. How far below the top of the glass does the bottom of the pool seem, as viewed from directly above?

(I) An earthquake P wave traveling 8.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 52° and the angle of refraction is 31°, what is the speed in the second medium?

(II) A sound wave is traveling in warm air (15°C) when it hits a layer of cold ( - 15° C) denser air. If the sound wave hits the cold air interface at an angle of 28°, what is the angle of refraction? The speed of sound as a function of temperature can be approximated by v = (331 + 0.60 T) m/s , where T is in °C.

A flashlight beam strikes the surface of a pane of glass (n = 1.56) at a 69° angle to the normal. What is the angle of refraction?

The label on a laser says it produces light of wavelength 670 nm. The laser beam passes through a block of plastic for which n = 1.57. What is the wavelength of the light inside the plastic?

Light from a laser (in air) strikes the exact center of one face of a solid glass cube (n = 1.40) at an angle θ relative to the normal. The refracted beam travels inside the glass until it strikes an adjacent face of the cube. The original angle of incidence θ is such that no light exits the cube where the beam strikes the second face. What is the maximum value θ can have?

A longitudinal earthquake wave strikes a boundary between two types of rock at a 41° angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus (Section 15–2)is the same for both types of rock, determine the angle of refraction.

"(II) A light ray is incident on an equilateral glass prism at a 45.0° angle to one face, Fig. 32–55. Calculate the angle at which the light ray emerges from the opposite face. Assume that n = 1.58.