An object emitting 500nm wavelength light moves away from you at half of the speed of light. What is the observed wavelengths of the light?
say c = 3 * 10^8
so v = 1.5* 10^8
moving away so looks longer
delta lambda/ lambda = v/c
d L = 500 nm (.5) = 250 nm
so
250 + 500 = 750 nm
To determine the observed wavelength of light emitted by an object moving away from you, we need to apply the principle of the Doppler effect. The Doppler effect describes the change in frequency (and therefore wavelength) of a wave as perceived by an observer when there is relative motion between the source of the wave and the observer.
In this case, the object is emitting light with a wavelength of 500 nm (nanometers) while moving away from you at half the speed of light.
The formula to calculate the observed or apparent wavelength of light is:
Observed Wavelength = Source Wavelength * (1 + (Relative Velocity / Speed of Light))
Let's plug in the values into the formula:
Source Wavelength = 500 nm
Relative Velocity = Half the Speed of Light = 0.5 * Speed of Light
The speed of light is approximately 3 x 10^8 meters per second.
Relative Velocity = 0.5 * (3 x 10^8 m/s) = 1.5 x 10^8 m/s
Now we can calculate the observed wavelength:
Observed Wavelength = 500 nm * (1 + (1.5 x 10^8 m/s) / (3 x 10^8 m/s))
Simplifying the equation:
Observed Wavelength = 500 nm * (1 + 0.5)
Observed Wavelength = 500 nm * 1.5
Observed Wavelength = 750 nm
Therefore, the observed wavelength of the light emitted by the object moving away from you at half the speed of light would be approximately 750 nm.