According to LambertSolutiondLL kdz Integrating lnL kz C

According to Lambert

dL/L = k*dz

Integrating :

ln|L| = kz + C
L = e^(kz + C)
L = De^(kz)

D = 1 ---> This is so because initially, 100% of intensity is maintained

L = e^kz)

1/2 = e^(10k)

-ln(2) = 10k

k = -ln(2)/10

L = e^(kz)

L = e^(-0.0693z)

Now, plug in L = 1/16 :

1/16 = e^(-0.0693 z)

-2.7725887 = -0.0693 * z

z = -2.7725887 / -0.0693

z = 40

So, the distance must be 40 feet