33. Geometric Optics

Suppose a ray of light starts in air, then enters a slab of diamond with parallel faces, and then exits again. If the ray entered the diamond at an angle ${\theta }_{\text{i}}$ from a line normal to the diamond slab, what is true of the final angle from normal ${\theta }_{\text{f}}$ ?

Light shines from a laser in air down into water. If the laser beam in air makes an angle of $40°$ with the water's surface, what angle will it make with the surface under water?

A graduated cylinder is filled with $14\mathrm{cm}$ of oil floating on $20\mathrm{cm}$ of water. How long, in nanoseconds, does it take light to travel from the top of the oil to the bottom of the water?

A light ray, moving in air, is incident on a piece of plastic at an angle of 23° with respect to the normal. Inside the plastic the ray travels at an angle of 16° with respect to the normal. What is the index of refraction of the plastic?

If oil is floating on water, what is the critical angle at the oil/water boundary?

What is the frequency of an electromagnetic wave that has the same wavelength as a 2.5 kHz sound wave in water?

A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Some modern optical devices are made with glass whose index of refraction changes with distance from the front surface. FIGURE P16.72 shows the index of refraction as a function of the distance into a slab of glass of thickness L. The index of refraction increases linearly from n₁ at the front surface to n₂ at the rear surface. b. Evaluate your expression for a 1.0-cm-thick piece of glass for which n₁ = 1.50 and n₂ = 1.60.

(a) A tank containing methanol has walls 2.50 cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 41.3° angle with the normal to the glass. Find the angle the light makes with the normal in the methanol. (b) The tank is emptied and refilled with an unknown liquid. If light incident at the same angle as in part (a) enters the liquid in the tank at an angle of 20.2° from the normal, what is the refractive index of the unknown liquid?

Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?

A light beam travels at 1.94 * 10^8 m/s in quartz. The wavelength of the light in quartz is 355 nm. (b) If this same light travels through air, what is its wavelength there?

A beam of light has a wavelength of 650 nm in vacuum. (b) What is the wavelength of these waves in the liquid?

The indexes of refraction for violet light λ = 400 nm2 and red light λ= 700 nm2 in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 53.5° to the normal. Calculate the angular separation between these two colors of light in the refracted ray.

As shown in Fig. E33.11

, a layer of water covers a slab of material X in a beaker. A ray of light traveling upward follows the path indicated. Using the information on the figure, find (b) the angle the light makes with the normal in the air.

A horizontal, parallelsided plate of glass having a refractive index of 1.52 is in contact with the surface of water in a tank. A ray coming from above in air makes an angle of incidence of 35.0° with the normal to the top surface of the glass.(a) What angle does the ray refracted into the water make with the normal to the surface?

A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum is I, find the intensity (in terms of I) of scattered light in the middle of (a) the red part of the spectrum.

A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 7.00 m from her. What is the depth of the water at this point?

The glass rod of Exercise 34.22 is immersed in oil (n = 1.45). An object placed to the left of the rod on the rod's axis is to be d 1.20 m inside the rod. How far from the left end of the rod must the object be located to form the ?

You're visiting the shark tank at the aquarium when you see a 2.5-m-long shark that appears to be swimming straight toward you at 2.0 m/s. What is the shark's actual speed through the water? You can ignore the glass wall of the tank.

A 4.0-m-wide swimming pool is filled to the top. The bottom of the pool becomes completely shaded in the afternoon when the sun is 20° above the horizon. How deep is the pool?

Shown from above in FIGURE P34.54 is one corner of a rectangular box filled with water. A laser beam starts 10 cm from side A of the container and enters the water at position x. You can ignore the thin walls of the container. a. If x=15 cm, does the laser beam refract back into the air through side B or reflect from side B back into the water? Determine the angle of refraction or reflection.

A horizontal laser beam enters the glass prism shown in FIGURE P34.55. When the laser beam exits the prism, by what angle will it have been deflected from horizontal?

A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle θ₂. Wavelengths for which the index of refraction is n + δn, where δn << n, are refracted at angle θ₂ + δθ. b. A beam of white light is incident on a piece of glass at 30°. Deep violet light is refracted 0.28° more than deep red light. The index of refraction for deep red light is known to be 1.552. What is the index of refraction for deep violet light?

A hydrogen discharge lamp emits light with two prominent wavelengths: 656 nm (red) and 486 nm (blue). The light enters a flint-glass prism perpendicular to one face and then refracts through the hypotenuse back into the air. The angle between these two faces is 35°. b. What is the angle (in degrees) between the red and blue light as it leaves the prism?