Answer:
ð/[2^(1/3)] + 1 or ð/2.26
Step-by-step explanation:
Step 1: Let the illumination be denoted as C
Let the two intensities be denoted as M and N respectively
Let the distance from point P to M be x and distance from P to N be (ð-x
Step 2:
Illumination at point P from M: Cm= kM/x^2
Illumination at point P from N: Cn= kN/(ð-x)^2
The sun of the illumination: Q=Cm+Cn = (kM/x^2) + (kN/(ð-x)^2)
Differentiate Q wrt x and equate to zero, we have
(-2kM/x^3) + [2kN/(ð-x)^3] = 0
Simplifying the above equation, we have
(ð-x)^3/x^3 = -2kN/-2kM
[(ð-x)/x]^3 = N/M
[(ð-x)/x] = (N/M)^(1/3)
ð-x = x[(N/M)^(1/3)]
ð = x[((N/M)^(1/3)) + 1]
Therefore, x = ð/[((N/M)^(1/3)) + 1]
Substitute M= ð/4 and N=ð/2 into equation above, we have
x = ð/[2^(1/3)] +1 or x = ð/2.26
