A triangular medium has varying refracting index `n = n_(0) + ax`, where x is the distance (in cm) along x-axis from origin and `n_(0) = (4)/(3)`. A ray is incident normally on face OA at the mid-point of OA. The range of a so that light does not escape through face AB when it falls first time on the face `AB(OA = 4 cm, OB = 3 cm and AB = 5 cm)` : (surrounding medium is air)

Options

A. `a gt(1)/(9)`
B. `a gt (2)/(9)`
C. `a gt(1)/(3)`
D. none of these

Answer

B

Explanation

Clearly, PM=3/2 cm
`37^(@) gt sin^(-1) 1/(n_(0) +a(3//2))`
`3/5 gt 1/(n_(0)+(3a)/2)`
`3n_(0)+(9a)/2 gt 5`
`(9a)/2 gt 1`
`a gt 2/9`