When we observe a wavelength of 594 nm instead of the rest wavelength of 600 nm, we can interpret this as a blue shift. A blue shift occurs when the source of light is moving towards the observer, causing the wavelength to decrease.
The difference between the observed wavelength (594 nm) and the rest wavelength (600 nm) indicates that the source is moving towards us. To understand how fast the source is moving, we can use the formula for redshift and blueshift:
z = (λobserved – λrest) / λrest
Plugging in our values:
z = (594 nm – 600 nm) / 600 nm = -0.01
The negative value of z indicates a blue shift. The velocity (v) can be approximated for small z by the formula:
v ≈ z * c
Where c is the speed of light (approximately 300,000 km/s). Therefore:
v ≈ -0.01 * 300,000 km/s = -3,000 km/s
This calculation shows that the source is approaching us, but it’s not moving at 10% or 1% of the speed of light. So, option a (the source is receding from us at 10% of the speed of light) and option b (the source is getting 1 hotter as we watch) are incorrect. However, option c (the source is approaching us at 0.1 of the speed of light) also does not hold up since our calculated speed is much smaller than 0.1 times the speed of light.
In summary, from the given data, we can conclude that the source is indeed moving towards us; however, none of the provided options accurately reflect this observation.