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Magazine Problem 72
A converging lens made of glass \((n=1.5)\) is placed under water \((n=1.33) .\) Describe how the focal length of the lens under water compares to the focal length in air. Draw a diagram to illustrate your answer.
Problem 73
An object \(8.0 \mathrm{cm}\) high forms a virtual image \(3.5 \mathrm{cm}\) high
located \(4.0 \mathrm{cm}\) behind a mirror. (a) Find the object distance. (b)
Describe the mirror: is it plane, convex, or concave? (c) What are its focal
length and radius of curvature?
Problem 74
A point source of light is placed \(10 \mathrm{cm}\) in front of a concave
mirror; the reflected rays are parallel. What is the radius of curvature of
the mirror?
Problem 75
A glass prism bends a ray of blue light more than a ray of red light since its index of refraction is slightly higher for blue than for red. Does a diverging glass lens have the same focal point for blue light and for red light? If not, for which color is the focal point closer to the lens?
Problem 76
A laser beam is traveling through an unknown substance. When it encounters a
boundary with air, the angle of reflection is \(25.0^{\circ}\) and the angle of
refraction is \(37.0^{\circ} .\) (a) What is the index of refraction of the
substance? (b) What is the speed of light in the substance?
(c) At what minimum angle of incidence would the light be totally internally
reflected?
Problem 77
In many cars the passenger's side mirror says: "Objects in the mirror are
closer than they appear." (a) Does this mirror form real or virtual images?
(b) since the image is diminished in size, is the mirror concave or convex?
Why? (c) Show that the image must actually be closer to the mirror than is the
object. (d) How then can the image seem to be farther away?
Problem 78
A scuba diver in a lake aims her underwater spotlight at the lake surface. (a)
If the beam makes a \(75^{\circ}\) angle of incidence with respect to a normal
to the water surface, is it reflected, transmitted, or both? Find the angles
of the reflected and transmitted beams (if they exist).
(b) Repeat for a \(25^{\circ}\) angle of incidence.
Problem 79
Laura is walking directly toward a plane mirror at a speed of $0.8 \mathrm{m}
/ \mathrm{s}$ relative to the mirror. At what speed is her image approaching
the mirror?
Problem 80
Xi Yang is practicing for his driver's license test. He notices in the
rearview mirror that a tree, located directly behind the automobile, is
approaching his car as he is backing up. If the car is moving at $8.0
\mathrm{km} / \mathrm{h}$ in reverse, how fast relative to the car does the
image of the tree appear to be approaching?
Problem 81
A plane mirror reflects a beam of light. Show that the rotation of the mirror
by an angle \(\alpha\) causes the beam to rotate through an angle \(2 \alpha\)
