refraction

let the minimum depth be x as mentioned in the question.
since vessel is cubical it is clear that i = 45°.
from snell's law sin r = sin45°μ ................→ r = sin ^-1(1μ√2)....................(1)

since angle QPD = 45°, PQ (=x) = QD
hence QO = x - b
now in ΔPQO
QO = x tan r or x - b = x tan r → x = \frac{b}{1- tanr}

substitute value of r from (1) will give the answer

Good work Manmay.

Bas ek baat samajh nahi aayi,,,,Light ki ray aankh se kaise nikal rahi hai....?! :P

Some supernatural eye it seems to be....!! [144]