286
Chapter 22
22.4
(a)
λ
0
8
7
300 10
10
550 10
==
×
×
=×
−
c
f
.
.
ms
5.45
Hz
m
14
(b)
From Table 22.1 the index of refraction for benzene is
n
=
1 501
.
. Thus, the wavelength in
benzene is
n
n
×
−
−
0
7
7
367 10
.
.
m
1.501
m
(c)
Eh
f
×
⋅
( )
×
( )
−
6 63 10
5 45
10
1
160
34
14
..
.
Js
H
z
eV
×
⎛
⎝
⎜
⎞
⎠
⎟
=
−
10
226
19
J
eV
.
(d)
The energy of the photon is proportional to the frequency, which does not change as the
light goes from one medium to another. Thus, when the photon enters benzene,
the energy does not change
.
22.5
The speed of light in a medium with index of refraction
n
is
v
=
cn
, where
c
is its speed in
vacuum.
(a)
For water,
n
=
1 333
.
, and
v
=
×
1 333
225 10
8
8
.
.
.
(b)
For crown glass,
n
=
152
.
, and
v
=
×
197 10
8
8
.
.
.
(c)
For diamond,
n
=
2 419
.
, and
v
=
×
2 419
124 10
8
8
.
.
.
22.6
(a)
From
fc
=
, the wavelength is given by
=
cf
. The energy of a photon is
f
=
, so the
frequency may be expressed as
fE
h
=
, and the wavelength becomes
=
c
f
c
hc
E
(b)
Higher energy photons have shorter waveleng
ths.
22.7
From Snell’s law,
nn
22
11
sin
sin
θθ
=
. Thus, when
θ
1
45
=°
and the ±
rst medium is air
(
n
1
100
=
.
), we have
sin
.
sin
2
2
45
= (
)
°
n
.
(a)
For quartz,
n
2
1 458
=
.
, and
2
1
1 458
29
=
()
°
⎛
⎝
⎜
⎞
⎠
⎟
−
sin
.s
i
n
.
(b)
For carbon disul±
de,
n
2
1 628
=
.
, and
2
1
1 628
26
=
°
⎛
⎝
⎜
⎞
⎠
⎟
−
sin
i
n
.
(c)
For water,
n
2
1 333
=
.
, and
2
1
1 333
32
=
°
⎛
⎝
⎜
⎞
⎠
⎟
−
sin
i
n
.