An equilateral prism deviates a ray through`23^(@)`for two angles of incidence differing by `23^(@)`find`mu`of the prism?

Answer

`(sqrt(43))/(5)`

Explanation

`A = 60^(@)`
i+e - 60 = `23^(@)` & e = i+ `23^(@)`
`2i + 23^(@) - 60^(@) = 23^(@)`
`i= 30^(@)`
`e = 53^(@) implies (1)/(2)= mu "sin"r_(1)`
`implies mu"sin"(60-r_(1)) = "sin"53^(@) = (4)/(5)`
`implies mu(sqrt(3))/(2). "cos"r_(1) - (1)- (1)/(2)."sin"r_(1)) = (4)/(5)`
`implies (sqrt(3)/(2)sqrt(1-sin^(2)r_(1))- (1)/(2)"sin"r_(1)) = (4)/(5)`
`implies mu(sqrt(3)/(2)sqrt(1-(1)/(4mu^(2)))- (1)/(2) xx (1)/(2mu)) = (4)/(5)`
`implies sqrt(3) sqrt(4mu^(2)-1) -1 = (4)/(5) xx 4 implies 4mu^(2) = ((21)/(5))^(2) (1)/(3)+ 1`
`implies mu = sqrt((1)/(4){(441)/(25 xx 3)+ 1}) = sqrt((129)/(75)) = sqrt(43)/(5)`