|Astronomy 110||PRINT Name   __________________________|
|Fall 2005   Section 006|| |
Homework 6 : Measuring Temperature
(Due Thursday, Oct 20, 2005)
The spectrum of sunlight, the "rainbow", is related to the ideal "black
body" spectrum, three of which are shown below. For a "black body" (an ideal
emitter), once you know the temperature, the amount of light emitted from each
square centimeter of its surface is known exactly. The three plots below are
the intensity of light as a function of wavelength in Angstroms for three black
bodies at different temperatures. The range of visible wavelenths of light is
also shown. Answer the questions on the back.
The visible region of the spectrum is marked by the dashed vertical lines in the figure. We can determine which dashed line is on the blue side and which is on the red side by looking at the wavelength scale at the bottom. In the diagram wavelength is increasing to the right, so that means blue will be on the left and red on the right, since blue light has shorter wavelengths than red light.
| ||       A      ||       B      ||       C      |
|Peak Wavelength in Angstroms||   2000   ||   5000   ||   10000   |
|Temperature in Kelvin||   15000   ||   6000   ||   3000   |
Calculate the temperatures of bodies A, B, and C and enter them in the table
We can rewrite the equation as:
and plug in the values that we measured off of the figure (which are listed in the table above). Note: this equation works for temperature in Kelvin and wavelength in Angstroms only, the constant 3 x 107 is different for different units.
There are a couple of ways to know this. Curve B peaks inside the visible spectrum, and the Sun is brightest in the visible part of the spectrum (in fact this is why our eyes are sensitive to this part in the first place). Another way to know that it is curve B is by knowing that the temperature of the Sun is about 5800 Kelvin, which is close to what we calculated for curve B.
To determine what color we see, we look at the curves in the visible part of the spectrum and ignore the rest. From problem 1, we know that the left vertical dashed line marks the blue wavelengths, and the right one marks the red wavelengths. Curve A is higher on the blue side than the red, so that means the hot body whose light curve is represented by curve A will look blue to us. Note: using this same logic we can tell that the hot body for curve C will look red, and the one for curve B will look yellowish because it is brightest somewhere between blue and red.