Prism geometry

The prism is an equilateral triangle, so its prism angle is $A = 60^\circ.$

It is given that minimum deviation occurs when the angle of incidence equals the prism angle: $i = A = 60^\circ.$

Condition for minimum deviation

For minimum deviation in a prism, $r_1 = r_2 = \frac{A}{2} = 30^\circ.$

Using Snell's law at the first face,

Find the distance from $P$ to $A$ inside the prism

Since $ABC$ is equilateral, let each side be $a$.

Point $P$ is the midpoint of $BC$, so $AP$ is the altitude of the equilateral triangle.

Hence, $AP = a\cos 30^\circ = a\cdot \frac{\sqrt3}{2}.$

From the figure, the side of the equilateral prism is $BC = 1\,\text{m}$, so $a=1\,\text{m}.$ Therefore, $AP = \frac{\sqrt3}{2}\,\text{m}.$

Speed of light inside prism

Speed of light in the prism is $v = \frac{c}{\mu} = \frac{3\times 10^8}{\sqrt3}\,\text{m/s}.$

Time taken from $P$ to $A$

Final integer

Therefore, the required number is $\boxed{50}.$

Comparison with stored answer

Stored correct answer is $5$, but the calculated value is $50$.

So I do not agree with the stored answer. It appears the exponent in the question is intended as $\times 10^{-10}$ s, in which case the coefficient should be $50$, not $5$.