A rod made of glass, `(mu = 1.5)` and of square cross-section is bent into the shape shown in figure. A parallel beam of light falls perpendicularly on the plane flat surface A. Referring to the diagram, d is the width of a side and R the radius of inner semi-circle. Find the maximum value of ratio `((d)/(R))` so that all light entering the glass through surface A emerge from the glass through B.

Answer

43467

Explanation

sin c = `(R)/(R+d) = (1)/(1.5) implies (R)/(R+d) gt (1)/(1.5)`
`implies (1)/(1 +d//R) gt (1)/(1.5) implies 1.5 gt 1 + (d)/(R) implies (d)/(R) lt (1)/(2)`