A rectangular block of glass is placed on a printed page lying on a horizontal surface. Find the minimum value of the refractive index of glass for which the letters on the page are not visible front any of the vertical faces of the block

A rectangular block of glass is placed on a printed page lying on a ho

1.	A rectangular block of glass is placed on a printed page lying on a horizontal surface. Find the minimum value of the refractive index of glass for which the letters on the page are not visible front any of the vertical faces of the block
Answer» SOLUTION :The situation is as shown in the Fig. Light will not emerge out from the vertical face BC if at it `I GT theta_c` or `sin I gt sin theta_c, sin I gt 1/ mu`……….(1) `1 TIMES sin theta=mu sin r` and in `Delta OPR` `r+i=90^@, r=90^@-i` SO `sin theta= mu sin (90^@-i)` `cos i= (sin theta//mu)` But `sin i=sqrt(1-cos^2 i)=sqrt(1-(sin theta//mu)^2)`.........(2) Substituting the value of SINI From eq (2) in (1) `sqrt(1-(sin^2 theta)/mu^2) gt 1/mu, mu^2 gt 1+ sin 2 theta` Now as `(sin^2 theta)_(max)=1`, `mu^2 gt 2, mu gt sqrt2` Hence `mu_(mi n)=sqrt2`