Question

why is the light from distant galaxies red - shifted?
they are moving toward us
the longer wavelengths are filtered out more by dust
they produce more red light than nearby galaxies
they are moving away from us

Explanation:

The red - shift of light from distant galaxies is due to the Doppler effect in the context of the expanding universe. Distant galaxies are moving away from us, and as they move away, the light waves they emit get stretched. This stretching of light waves increases their wavelength, and light with longer wavelengths appears redder. Let's analyze the options:

• Option "They are moving toward us": If a galaxy is moving toward us, the light would be blue - shifted, not red - shifted. So this is incorrect.
• Option "The longer wavelengths are filtered out more by dust": Dust filtering doesn't cause the overall red - shift of distant galaxies. The red - shift is a result of the motion of the galaxies, not dust filtration. So this is incorrect.
• Option "They produce more red light than nearby galaxies": Galaxies don't inherently produce more red light just because they are distant. The red - shift is a result of their motion, not their light - production properties. So this is incorrect.
• Option "They are moving away from us": As distant galaxies move away from us, the light waves are stretched (Doppler effect for light in an expanding universe), leading to an increase in wavelength and thus a red - shift. This is the correct explanation.

Answer:

The correct option is "They are moving away from us" (the last option among the given choices).