286
Chapter 22
22.4
(a)
λ
0
8
7
3 00
10
10
5 50
10
=
=
×
×
=
×
−
c
f
.
.
m s
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
λ
λ
n
n
=
=
×
=
×
−
−
0
7
7
5 50
10
3 67
10
.
.
m
1.501
m
(c)
E
hf
=
=
×
⋅
(
)
×
(
)
−
6 63
10
5 45
10
1
1 60
34
14
.
.
.
J
s
Hz
eV
×
⎛
⎝
⎜
⎞
⎠
⎟
=
−
10
2 26
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
=
c n
, where
c
is its speed in
vacuum.
(a)
For water,
n
=
1 333
.
, and
v
=
×
=
×
3 00
10
1 333
2 25
10
8
8
.
.
.
m s
m s
(b)
For crown glass,
n
=
1 52
.
, and
v
=
×
=
×
3 00
10
1 52
1 97
10
8
8
.
.
.
m s
m s
(c)
For diamond,
n
=
2 419
.
, and
v
=
×
=
×
3 00
10
2 419
1 24
10
8
8
.
.
.
m s
m s
22.6
(a)
From
λ
f
c
=
, the wavelength is given by
λ
=
c f
. The energy of a photon is
E
hf
=
, so the
frequency may be expressed as
f
E h
=
, and the wavelength becomes
λ
=
=
=
c
f
c
E h
hc
E
(b)
Higher energy photons have shorter waveleng
ths.
22.7
From Snell’s law,
n
n
2
2
1
1
sin
sin
θ
θ
=
. Thus, when
θ
1
45
=
°
and the first medium is air
(
n
1
1 00
=
.
), we have
sin
.
sin
θ
2
2
1 00
45
=
(
)
°
n
.
(a)
For quartz,
n
2
1 458
=
.
,
and
θ
2
1
1 00
45
1 458
29
=
(
)
°
⎛
⎝
⎜
⎞
⎠
⎟
=
°
−
sin
.
sin
.
(b)
For carbon disulfide,
n
2
1 628
=
.
,
and
θ
2
1
1 00
45
1 628
26
=
(
)
°
⎛
⎝
⎜
⎞
⎠
⎟
=
°
−
sin
.
sin
.
(c)
For water,
n
2
1 333
=
.
,
and
θ
2
1
1 00
45
1 333
32
=
(
)
°
⎛
⎝
⎜
⎞
⎠
⎟
=
°
−
sin
.
sin
.