Question

A ray of light travels from a medium of refractive index u to air. It's angle of incidence in the medium is theta

Answer 1

░▒▓█►─═ ʜᴇʀᴇ ɪs ʏᴏᴜʀ ᴀɴsᴡᴇʀ ═─◄█▓▒░

Let the angles of incidence and refraction be I and R respectively. By Snell’s law, sin(I)=ρsin(R) where ρ is the refractive index. In your case sin(I)=sin(2R)=2sin(R)cos(R), so ρ=2cos(R).

And that is as far as you can go without knowing ρ. Knowing ρ gives you cos(R) and hence gives you sin(R) and hence sin(I). Conversely, if you know I or R you can find ρ.

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