# 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.

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