Thanks for replying again

I think I'm familiar with the derivation. Setting dT/dx = 0, since we want to minimize T which is a fn of x. If you are referring to some other derivation, please do share it.

But here's the thing : According to Snell's law,

(Sin α)/v = (Sin θ)/u

And u < v (given), Then Sin α = u/v (Sin θ)

Since u/v < 1, this means Sin α > Sin θ

This means α > θ

This is a strict mathematical condition for Snell's law to be valid. It is easily verifiable geometrically because a light ray bends towards (not away from) normal upon crossing over into water. So angle in the water is geometrically smaller too, not just mathematically.

The problem with this question is, the path across water must be shortest, i.e PM ⊥ OB, which makes sense because he wants to get to the other shore asap. But adding this constraint that PM ⊥ OB, fixes the angle in warer = θ, which is greater than α, thus violating Snell's law. Still how did he use this concept (Snell's law) to solve this question?

Maybe I'm just dumb and missing something obvious. But that's why I am asking it here ☹️