Find the angle of minimum deviation produced by an equilateral prism of refractive index 1.55. Also find the angle of minimum deviation when the prism is completely immersed in water (n=1.33)

(D_m)= 2r= A

So, (D_m)= 2(i-r) (You already know)

Now, 2r= 2(i-r)

Finally, i= 2r

Now, the refractive index given in the question is 1.5

So, {sin (i)}/{sin (r)}= 1.5

Now putting the value of i as 2r in the above equation, we get-

{sin (2r)}/{sin (r)}= 1.5

On using the “Sine Addition formula”,

2{cos (r)}= 1.5

So, {cos (r)}= 0.75

So, r= 41^o approx