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Midterm Exam
7 October 2010
For full credit you must show your work!
Problem 1 (5 points).
In round numbers, the human body temperature is about 100°F.
What is the wavelength of our maximum thermal emission?
Answer:
Wien’s law tells us that the wavelength of maximum emission is given by:
λ
max
~2897 / T
where T is in degrees K and the wavelength is in units of
μ
m.
Convert 100°F to K:
deg K = (100 – 32) / 1.8 + 273 = 311 K.
λ
max
= 2897/311 =
9.3
μ
m
Problem 2 (10 points).
Define “emissivity” and “absorptivity”, and give a statement of
Kirchhoff’s Law. Use words, not mathematical equations.
Answer:
Emissivity is the amount of radiation emitted by an object relative to the amount
emitted by a blackbody at the object’s temperature.
Absorptivity is the amount of radiation absorbed by an object relative to the
amount incident on the object.
Kirchhoff’s law states that for an object in thermodynamic equilibrium, the
emissivity is equal to the absorptivity.
Problem 3 (10 points).
In the visible, the real index of refraction is ~1.33 for water and
1.0 for air. For visible light traveling from water to air, at what incidence angle on the
water/air interface will total internal reflection occur?
Answer:
The critical angle (
Θ
), above which total internal reflection occurs for
light passing from a medium with index of refraction N
1
into a medium with
index of refraction N
2
, is
Θ
= arcsin(N
2
/N
1
).
For light traveling from water to air
this is arcsin(1/1.33) = 48.8°.
Problem 4 (15 points)
. The solar irradiance at the top of the Earth’s atmosphere is 1361
W m
2
. Using only this information and information provided on the equation sheet,
calculate the temperature of the surface of the sun.
Answer:
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This note was uploaded on 01/19/2011 for the course ATOC 5235 taught by Professor Randell during the Fall '10 term at Colorado.
 Fall '10
 Randell

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