Page 394 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 30] LIGHT 379

where v 1 and n 1 are, respectively, the velocity of light and index of refraction of the first medium and v 2 and n 2
are the corresponding quantities in the second medium. Snell’s law is often written

n 1 sin i = n 2 sinr
In general, the index of refraction of a medium increases with increasing frequency of the light. For this
reason a beam of white light is separated into its component frequencies, each of which produces the sensation
of a particular color, when it passes through an object whose sides are not parallel, for instance, a glass prism.
The resulting band of color is called a spectrum (Fig. 30-8).

Glass
prism
Screen
White
light Red
Orange
Yellow
Green
Blue
Violet

Fig. 30-8. (From Konrad B. Krauskopf and Arthur Beiser, The Physical Universe, 10th Ed., c 2003, The McGraw-
Hill Companies. Reproduced with permission of The McGraw-Hill Companies.)

SOLVED PROBLEM 30.11

Why is a beam of white light that passes perpendicularly through a flat pane of glass not dispersed into
a spectrum?
Light incident perpendicular to a surface is not deflected, so light of the various frequencies in white light stays
together despite the different velocities in the glass.

SOLVED PROBLEM 30.12

The index of refraction of diamond is 2.42. What is the velocity of light in diamond?
Since n = c/v, here
8
c 3 × 10 m/s 8
v = = = 1.24 × 10 m/s
n 2.42
SOLVED PROBLEM 30.13
A beam of light enters a lake at an angle of incidence of 40 . Find the angle of refraction. The index of
◦
refraction of water is 1.33.
Here medium 1 is air and medium 2 is water. From Snell’s law,
1.00
n 1 ◦ ◦
sinr = sin i = sin 40 = 0.483 r = 29
n 2 1.33
The angle of refraction is less than the angle of incidence because n 2 > n 1 .

SOLVED PROBLEM 30.14
A lantern held by a submerged skin diver directs a beam of light at the surface of a lake at an angle of
◦
incidence of 40 . Find the angle of refraction.