The Doppler Effect and Redshifting ?

[klvoss]

If I could please get some help on these really puzzling questions, that would be great.

Consider these formulas:

If a light source with frequency fo is moving away at speed v, then you see the frequency to be lower according to
f=fo( (the square root of 1-(v/c)) / (the square root of 1+(v/c) )

If a light source is moving towards you, the frequency is shifted higher according to
f=fo( (the square root of 1+(v/c)) / (the square root of 1-(v/c) )

A) Now using the relationship, c=f X lambda, what is the formula for how the wavelength of light shifts when the light source is moving toward you or away from you?

B) If our eyes are sensitive to yellow light, then if the frequency/wavelength of light changes by a factor of 2 in either the upwards or downwards direction, we can no longer see the light because the wavelength of the light becomes either too long or too short for our eyes to detect. So how fast do we have to move with respect to the sun before we can no longer see it with our eyes?

C) Suppose you are driving toward a traffic light that is currently red. How fast would you have to drive so that the red light emitted by the traffic signal appears to you as green light? Wavelength of red light = 8000 Angstroms, green light = 5000 Angstroms.

D) Suppose you are in a spaceship and a laser beam is chasing you; the beam is destined to catch up to you.
1) Your spaceship is traveling at 1/2 the speed of light.
2) Your spaceship is traveling at 3/4 the speed of light.
In which case does the laser beam do more damage to your ship, or are they the same? Think in terms of the speed and the energy of the laser beam as observed by your spaceship. The energy of light particles are determined by the relationship E=hf=(hc)/lambda, where h=6.63X10^-23 erg/sec

 

[jbsteele]

.A) When the light source is moving away from you, the wavelength of light shifts according to λ=λo ( (the square root of 1-(v/c)) / (the square root of 1+(v/c) )When the light source is moving towards you, the wavelength of light shifts according toλ=λo ( (the square root of 1+(v/c)) / (the square root of 1-(v/c) )B) In order for us to no longer be able to see the sun with our eyes, we would need to move away/towards it at a speed of approximately 0.29c. This is calculated by taking the ratio of the wavelength of yellow light (590 nm) and dividing it by two, then solving for v using the equation v=(c)(f2/f1-1), where c is the speed of light and f1 and f2 are the initial and shifted frequency of the light, respectively.C) To make the red light emitted by the traffic signal appear as green light, we would need to drive towards the signal at a speed of approximately 0.99c. This is calculated by taking the ratio of the wavelength of green light and red light (5000/8000 Angstroms), then solving for v using the equation v=(c)(f2/f1-1). D) In the first case, when the spaceship is traveling at ½ the speed of light, the laser beam will do more damage to the ship because its energy will be higher as observed by the spaceship. This is because the laser beam is chasing the ship and so its frequency and energy will be shifted upwards according to the formula E=hf=(hc)/λ, where h=6.63X10^-23 erg/sec. In the second case, when the spaceship is traveling at ¾ the speed of light, the laser beam will do the same amount of damage to the ship because its energy will remain the same as observed by the spaceship.

 

[nlightner]

, c=3X10^10 cm/sec, and f is the frequency of light.

A) The formula for how the wavelength of light shifts when the light source is moving towards or away from you is:

λ' = λ √(1 ± v/c) where λ' is the shifted wavelength, λ is the original wavelength, and v is the speed of the light source.

B) If the frequency/wavelength of light changes by a factor of 2, then the speed of the light source must be equal to or greater than the speed of light (c) for us to no longer see it. This means that we would have to be moving at nearly the speed of light relative to the sun in order for it to become invisible to us.

C) To see the red light as green, the wavelength must shift from 8000 Angstroms to 5000 Angstroms. Using the formula from part A, we can set up the following equation:

5000 = 8000 √(1 + v/c)

Solving for v, we get v = 1/3 c. This means that you would have to be moving at 1/3 the speed of light towards the traffic light in order for the red light to appear green.

D) The energy of the laser beam is determined by its frequency and wavelength, which are both affected by the Doppler Effect. As your spaceship moves, the frequency and wavelength of the laser beam will shift accordingly. In both cases, the laser beam will have a higher frequency and shorter wavelength when it reaches your spaceship, making it more damaging. However, the laser beam will have a slightly higher energy when your spaceship is traveling at 3/4 the speed of light compared to 1/2 the speed of light. This is because the frequency shift is greater at higher speeds. Therefore, the laser beam will do slightly more damage when your spaceship is traveling at 3/4 the speed of light.