# Homework Help: Derive a final formula from two other formulas

1. Apr 27, 2010

### MWidhalm18

Using these two formulas derive the third formula:

D/l = (D+f)/(l+alpha)
D/r = (D+f)/(r+beta)

D=(fb)/(alpha+beta)

where D is the distance of the point from the line between the viewer's eyes;
f is the focal length of the lens in the eye; b is the distance between the two eyes;
and the sum of the terms α and β is referred to as the disparity.

Is this right?
1. D/l=(D+f)/(l+alpha) --> flip --> l/D=(l+alpha)/(D+f)
2. D/r=(D+f)/(r+beta) --> flip --> r/D=(r+beta)/(D+f)

(l+r)/D=((l+alpha)+(r+beta))/(D+f)

l+r=b

b/D=(b+alpha+beta)/(D+f)

cross multiply

b(D+f)=D(b+alpha+beta)
bD+bf=Db + Dalpha + Dbeta
bf = Db+Dalpha+Dbeta-bD
bf=Dalpha + Dbeta
bf = D(alpha+beta)

D = bf/(alpha+beta)

Last edited: Apr 27, 2010