A rectangulat block of refractive index `mu` is placed on a printed page lying on a horizontal surface as shown in Fig. , Find the minimum value of `mu` so that the letter L on the page is not visible from any of the vertical sides.

Explanation

The situation is depicted in figure. Light will not emerge out from the vertical face `BC` if at it `I gt theta_(C) "or" "sin"I gt "sin" theta_(C) implies "sin"I gt (1)/(mu) [ "as sin theta_(C)= (1)/(mu)] … (i)`
But from Snell's law at `O 1 xx "sin" theta= mu "sinr`
And in `DeltaOPR , r + 90 + i = 180 implies r + i = 90^(@) implies r = 90 - i`

So `"sin"theta = mu "sin"(90-i) = mu"cos"i implies "cos"i = ("sin"theta)/(mu)`
so `"sin"i = sqrt(1-cos^(2)i) = sqrt(1-[("sin"theta)/(mu)]^(2)) .... (ii)`
so substituting the value of sin i from equation (ii) in (i),
`sqrt(1- (sin^(2)theta)/(mu^(2))) gt (1)/(mu)` i.e., `mu^(2) gt 1 + sin^(2)theta`
`because (sin^(2)theta)_(max) = 1 therefore mu^(2) gt 2 sqrt(2) therefore mu_(min) = sqrt(2)`