1. Color depends on the frequency of light. For example the frequency of red lig
ID: 2872186 • Letter: 1
Question
1. Color depends on the frequency of light. For example the frequency of red light is between 400 and 484 and the frequency of yellow light is between 508 and 526. You can see some frequencies better than other frequencies. For example humans cannot see infrared light which has a frequency below 214. Suppose the following curve gives a measure of how well humans can see each frequency with a higher value meaning it is easier to see that frequency.
Suppose the equation for the ability to see a frequency is given by f(x) = 2000x - 2x^2 - 400000
Find the value of X, the frequency that humans can see the best, that maximizes f(x)
[It turns out that the sun’s highest output is close to this frequency. You eye is basically optimized to match the sun’s output.]
2. Consider the function: f(x) = x^3 - 3x^2 - 3x - 1
3.
3. The Lorentz Factor is given by the equation: .
Find f(0), f(.1), f(.5), f(.99).
Einstein use the Lorentz Factor in the Theory of Relativity. In the Theory of Relativity we let X = v/c where v is the velocity (speed) you are going and c is the Speed of Light. If you are traveling at 10% of the Speed of Light, v = .1c then X = (.1c)/c = .1. According to the Theory of Relativity the faster you go the more you weigh according to the Lorentz Factor so
where X = v/c. If a man weighs 160 pounds when he is not moving, find his weight if he is moving at 10% of the Speed of Light, at 50% of the Speed of Light, at 99% of the Speed of Light. From this why do physicists say you a man cannot go at the Speed of Light?
Explanation / Answer
1) f(x) = 2000x - 2x^2 - 400000
f '(x) = 2000 -4(x)
equate f '(x) to zero
==> f '(x) = 0
==> 2000 -4(x) = 0
==> 4x = 2000
==> x = 2000/4
==> x = 500
Now f ''(x) = -4 ==> f ''(500) = -4
Since f ''(x) < 0 , at x = 500 function is maximum at x = 500
hence frequency at which human beings can see best is 500
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