33. Geometric Optics

Both surfaces of a double convex lens have radii of 31.4 cm. If the focal length is 26.3 cm, what is the index of refraction of the lens material?

A light ray in air is incident on a transparent material whose index of refraction is n. Find an expression for the (non-zero) angle of incidence whose angle of refraction is half the angle of incidence.

(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?

A laser pointer emits a ray which enters a quartz crystal at an angle 50° with the normal to the surface of the crystal. The ray bends inside the crystal, making an angle of 30° with the normal. Find the index of refraction of quartz.

Light traveling in air is incident on the surface of a block of plastic at an angle of 62.7° to the normal and is bent so that it makes a 48.1° angle with the normal in the plastic. Find the speed of light in the plastic.

"(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.

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?

The 80-cm-tall, 65-cm-wide tank shown in FIGURE P34.48 is completely filled with water. The tank has marks every 10 cm along one wall, and the 0 cm mark is barely submerged. As you stand beside the opposite wall, your eye is level with the top of the water. Can you see the marks from the top of the tank (the 0 cm mark) going down, or from the bottom of the tank (the 80 cm mark) coming up? Explain.

A ray of light is incident on a glass pane with an angle of 60°. The light partially reflects and partially refracts. What is the angle θ between the reflected and refracted rays?

(II) A beam of light in air strikes a slab of glass (n = 1.62) and is partially reflected and partially refracted. Determine the angle of incidence if the angle of reflection is twice the angle of refraction.

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°. What is the angle (in degrees) between the red and blue light as it leaves the prism?

(I) What is the speed of light in (a) ethyl alcohol, (b) lucite, (c) crown glass?

To a fish in an aquarium, the 4.00-mm-thick walls appear to be only 3.50 mm thick. What is the index of refraction of the walls?

We wish to determine the depth of a swimming pool filled with water by measuring the width (x = 5.20m) and then noting that the bottom edge of the pool is just visible at an angle of 13.0° above the horizontal as shown in Fig. 32–61. Calculate the depth of the pool.

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(I) A diver shines a narrow flashlight beam upward from beneath the water at a 32.8° angle to the vertical. At what angle does the light leave the water?