Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is `mu`, a ray, incident at an angle `theta`, on the face AB would get transmitted through the face AC of the prism provided:

Options

A. `theta gt sin^-1[ mu sin(A - sin^-1((1)/(mu)))]`
B. `theta lt sin^-1 [mu sin(A - sin^-1((1)/(mu)))]`
C. `theta gt cos^-1 [mu sin(A - sin^-1((1)/(mu)))]`
D. `theta lt cos^-1 [mu sin(A - sin^-1((1)/(mu)))]`

Answer

A

Explanation

Here, `mu = (sin i_1)/(sin r_1), As i_1 = theta`
`sin theta = mu sin r_1`
or `sin r_1 = (sin theta)/(mu)` or `r_1= sin^-1 ((sin theta)/(mu))`
As `r_1 + r_2 = A`,
`:. r_2 = A - r_1` or `r_2 = A - sin^-1 ((sin theta)/(mu))`
This shows, `r_2 lt sin^-1 ((1)/(mu))`
`A - sin^-1((sin theta)/(mu)) lt sin^-1 ((1)/(mu))`
or `A - sin^-1 ((1)/(mu)) lt sin^-1 ((sin theta)/(mu))`
or `sin (A - sin^-1((1)/(mu))) lt (sin theta)/(mu)`
or `mu xx sin (A - sin^-1((1)/(mu))) lt sin theta`
or `theta gt sin^-1 [mu sin {A - sin^-1 ((1)/(mu))}]`.
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