The answer is 3.414213562.

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## So we get $i=2r$

## $\frac{sin(i)}{sin(r)}$ = $n$

## $2cos(r)=n$

## $sin(i)=$ $\frac{d}{r}$

## $sin(2r)=$ $\frac{d}{r}$

## Now using simple algebraic manipulation we get that $\frac{n^2}{2}$ = $\frac{r+\sqrt{r^2-d^2}}{r}$

## $0<d<=r$

## Hence $\sqrt{2}<n<=2$ .So the answer is $\sqrt{2}+2=3.414213562$

NOTE:THIS IS INPHO 2007 QUESTION SO NO CLAIM OF ORIGINALITY IS MADE