A glass vessel in the shape of triangular prism {XYZ} is filed with water and light is incident normaly on the face XY. If the refractive indices of water and glas is 4/3 and 3/2,total internal reflection will ocur at the glass-air surface only for sin¥ greater than _____?[¥=angle of prism]

draw a prism XYZ with verticle angle Y = angle of prism

now draw a ray which is passing  through XY & touching XZ....

at XZ let its angle with normal is i...

applying snells law

  sini/sinr = n_g/n_w = 3/2/4/3=9/8 ............1

now this ray is making an angle r with normal of glass surface ...     

again applying snells law

sinr/sinr₁ = n_air/n_{g                               (angle of incidence is r)}

sinr/sin90 >or= 1/3/2                       (for total internal reflaction ,r₁ = 90)

sinr = or > 2/3                           

from eq 1

8sini/9 >or=2/3

 sini >or=3/4      ............................2

now find relation in bw i(angle of incidence) & Y(angle of prism) by using geometry  & put in eq 2

Approved