A rod of glass `( mu = 1.5)` and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of `(d)/(R)` light entering the glass slab through surface A emerges from the glass through B

Options

A. 1.5
B. 0.5
C. 1.3
D. None of these

Answer

B

Explanation

`theta ge i_(c )`
`rArr " " theta ge sin^(-1) ((1)/(n)) rArr sin theta ge t(1)/(n) `
Now, sin `theta = (R )/(R + d) `
`(R )/(R + d) ge (1)/(n) rArr 1 + (d)/(R ) le n `
`rArr (d)/(R ) le n -1 rArr ((d)/(R ))_(max) = 0.5 `