Answer 1

When the prism is kept in another medium we have to take the refractive index of the prism with respect to the provided medium. 

`"medium"^μ = ("μ"_"prism")/("μ"_"medium") = sin[((A + D_m)/2)]/sin(A/2)`

`1.6/((4sqrt(2))/5) = sin[((60^circ + D_m)/2)]/sin(60^circ/2)`

`sqrt(2) = sin[((60^circ + D_m)/2)]/(1/2)`

`sin^-1(1/sqrt(2)) = ((60^circ + D_m)/2)`

`90^circ = 60^circ + D_m`

`D_m = 30^circ`