For a given incident ray as shown in Fig., the condition of total internal reflection of ray will be satisfied if the refractive index of the block will be.
.

Options

A. `(sqrt(3) + 1)/(2)`
B. `(sqrt(2) + 1)/(2)`
C. `sqrt((3)/(2))`
D. `sqrt((7)/(6))`

Answer

C

Explanation

As shown in Fig. `r + C = 90^(@)`,
`r = (90^(@) - C)`
As `mu = (sin i)/(sin r) = (sin 45^(@))/(sin (90^(@) - C)) = (1)/(sqrt(2) cos C)`


Again, `mu = (1)/(sin C), sin C = (1)/(mu) = sqrt(2) cos C`
`tan C = sqrt(2)`,
`:. sinC = sqrt((2)/(3)) or mu = (1)/(sin C) = sqrt((3)/(2))`