Graphics Reference
In-Depth Information
function of
T
(i.e., for fixed
T
, find the
f
that maximizes power). Show that this
is roughly linear in
T
. (This is known as
Wien's displacement law.
)Todoso,fix
T
, and define a variable
u
=
f
T
, and write
R
(
f
,
T
)
as a function
S
(
u
)=
T
3
u
3
/
D
(
u
)
,
where
D
(
u
)=
e
(
h
/
k
)
u
1, which depends only on the single variable
u
. Under
what condition on
u
is
S
(
u
)
a maximum? (You may assume that
e
(
h
/
k
)
u
−
1.)
For
T
near 10,000
◦
K (roughly the temperature of the surface of the sun),
the peak is at about frequency 5
>>
10
14
Hz, which is just about in the middle of
the range of visible light (roughly 4
×
10
14
Hz); this means that
the human visual system is most sensitive to the energy that's most common (sun-
light).
10
14
Hz to 7
×
×