In an experiment for determination of refractive index of glass of a prism by `i-delta`, plot it was found thata ray incident at angle `35^circ`, suffers a deviation of `40^circ` and that it emerges at angle `79^circ`. In that case which of the following is closest to the maximum possible value of the refractive index?

Options

A. `1.5`
B. `1.6`
C. `1.7`
D. `1.8`

Answer

A

Explanation

Here, `i_1 = 35^@, delta = 40^@, i_2 = 79^@, mu = ?`
As `A + delta = i_1 + i_2`
`A= (i_1 + i_2) - delta = 35^@ + 79^@ - 40^@ = 74^@`
`mu = (sin(A + delta_m)//2)/(sin A//2) = (sin(74^@ + 40^@)//2)/(sin 74^@//2)`
`=(sin 57^@)/(sin 37^@) = (0.8386)/(0.6018) ~= 1.4`
Here, we have assumed that `delta_(min) = 40^@` which may not be true. Hence maximum possible value of `mu` will be closest to `1.5`.