Optics in Swimming Pool

(As shown in figure) Let an Stone " O " is Placed at the bottom of swimming Pool of depth H and the refractive index index of water is \(\mu \) this stone is viewed by an man at an angle \(\theta \) then what will be the apparent depth ( h ) of this stone from water surface ?

If the apparent depth \(h\) can be expressed as :

\[h = \cfrac { \alpha { (\cos { \theta } ) }^{ a } }{ \mu { H }^{ b } } { ({ H }^{ c } + { x }^{ d }) }^{ \frac { e }{ f } }.\]

then compute the value of \( \alpha + a + b + c + d + e + f \).

Details and Assumption
\(gcd(e,f) = 1\).
\( \alpha, a, b, c, d, e, f \) are all positive integers.

This is part of my set Deepanshu's Mechanics Blasts
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