1.

When a light ray centers a refracing medium, it is found that the magnitude of the angle of refraction is equal to half the angle of reflection. If mu is the refractive index of the medium, then the angle of incidence is

Answer»

`2sin^(-1)((MU)/(2))`
`2cos^(-1)((mu)/(2))`
`cos^(-1)((mu)/(2))`
`sin^(-1)((mu)/(2))`

Solution :ACCORDING to GIVEN problem,
Angle of refraction = `(1)/(2)` (Angle of reflection)
or `R.=(1)/(2)r`
As `mu=(sini)/(sinr)` (where i is the angle of incidence)
`mu=(sinr)/(sin((1)/(2)r))( :. "Angle of incidence", i= "Angle of refraction", r)`
`mu=(sinr)/(sin((1)/(2)r))( :. "Angle of incidence", i= "Angle of refraction", r)`
`cos^(-1)((mu)/(2))=(r)/(2)` or `r=2cos^(-1)((mu)/(2))`
`:.i=r :.i=2cos^(-1)((mu)/(2))`


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