Given that the angle of minimum deviation for a colour is `43^(@)`48' and its RI = 1.588, Calculate refracting angle of the prism.

Explanation

`D=43^(@)48., n=1.588`
`n=(sin((A+D)//2))/(sinA//2)`
`=(sin(A//2+(43^(@)48.)//2))/(sinA//2)`
`=(sin(A//2 +21^(@)54.))/(sinA//2)`
`1.588=(siniA//2cos21^(@)54.+sin21^(@)54.cosA//2)/(sinA//2)`
`1.588=cos21^(@)54.+sin21^(@)54.+sin21^(@)54. (1)/(tanA//2)`
`=0.9278+0.3730+(1)/(tanA//2)`
`0.6602=0.3730xx(1)/(tanA//2)`
`tanA//2=0.5649`
`A//2=29^(@)28.`
`therefore A=58^(@)56.`