# Homework Help: Two lens systems

1. Jul 5, 2010

### Neophyte

1. The problem statement, all variables and given/known data
Two Lens systems:
Lens one is a diverging lens and lens two is converging

O1 (object distance) = 9.6 cm
Focal length F1= 6.5 cm
distance between the two lenses is 13 cm
F2 = 7.4 cm
Find the image distance i2 for the image produced by lens 2 (the final image produced by the system) and the overall lateral magnification M for the system, including signs.

2. Relevant equations

1/i + 1/o = 1/f

3. The attempt at a solution

i1 = 20.13 cm
o1=9.6 cm
i2=
o2=1/

i1
(1/6.5) - (1/9.6) = 1/i = 0.049

i1 = 20.129

o2
d = 13 cm
o2 = d - i1
o2 = 13 - 20.129
o2 = -7.129 cm

i2

1/i =(1/7.4) - (1/-7.129)
i2 = 3.63 cm

Anyways I keep getting this incorrect but I am not sure what is wrong I think I mess up solving for the object2 but I have no idea.

2. Jul 5, 2010

### Staff: Mentor

Where is the image from lens 1 alone? Show how you'd calculate that.

3. Jul 5, 2010

Hello neophyte,for your diverging lens the focal length should be given a negative value and for your converging lens it should be given a positive value.

4. Jul 5, 2010

### Neophyte

-(1/f) - (1/O) = (1/i)
-(1/6.5) -(1/9.6) = 1/i = 0.258

i1 = -3.87

d = 13 cm
o2 = d - i1
o2 = 13 +3.875
o2 = 16.875 cm

1/i2 = (1/f) - (1/o2)
1/0.07587 = (1/7.4) - (1/16.875)
i2 = 13.179

Thank you both