Light travels a distance x in time in t₁ air and 10x in time t₂ in another denser medium. What is the critical angle for this medium? 

Velocity of light in air = (x/t₁)
Velocity of light in denser medium =$=\frac{10\mathrm{x}}{{\mathrm{t}}_2}=\mathrm{v}$
If critical angle is c,
$\begin{array}{l}\sin \mathrm{c}=\frac{\text{ Velocity in denser }}{\text{ Velocity in rarer }}=\frac{\frac{10\mathrm{x}}{{\mathrm{t}}_2}}{\frac{\mathrm{x}}{{\mathrm{t}}_1}}=\frac{10{\mathrm{t}}_1}{{\mathrm{t}}_2}\\ \mathrm{c}={\sin }^{-1}\left(\frac{10{\mathrm{t}}_1}{{\mathrm{t}}_2}\right)\end{array}$