Question

An opaque cylindrical tank with an open top has a diameter of $3.00m$and is completely filled with water. When the setting sun reaches an angle of ${37}^o$ above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is tank in tank?

Answer 1

$h=depth,angleincidenttonormal=aangleofreflection=b,a=90-37={53}^{0}UsingSnellslaw;\left(n\right)air\times sin{53}^0=\left(n\right)water\times sin\left(b\right)\_\_\_\_\left(i\right)eqnforair=1nforwater=1.33puttinginequation\left(i\right)aboveb=1\times \frac{0.79}{1.33}b=36.86Nowtan\left(b\right)=\frac{d}{h}h=\frac{3}{tan\left(36.86\right)}h=4.00\simeq 4m$