When light from outer space, after bouncing off(reflection) several times and refracting several times reaches the surface of the earth and gets detected. Which field of study of physics deals with this?(Astronomy,Astrophysics or Cosmology)?
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It's my understanding (anyone more knowledgeable, please correct me if I'm off) that astronomy is the act of observing space, astrophysics is the act of explaining astronomical observation with physics, and cosmology is a branch of astrophysics focusing on very large scales (mostly, properties of the universe as a whole). So, what you've described would be astronomy, as you make no mention of physical analysis of the data.
I agree with what Bong said, the act of observation is astronomy.
Astrophysics and cosmology are more theoretical and and try to explain what is observed.
Sometimes the theories give the astronomers ideas what to look for.
The discovery of gravitational lenses is an example.