Solving Two Lens System: O1, F1, F2, i2, M

[Neophyte]

Homework Statement

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.

Homework Equations

1/i + 1/o = 1/f

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.

 

[Doc Al]

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

 

[Dadface]

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.

 

[Neophyte]

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

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

i1 = -3.87

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.

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

 

[rwisz]

Your attempt at a solution is on the right track, but there are a few errors in your calculations. First, your calculation for i1 is incorrect. The correct equation to use is 1/i1 + 1/o1 = 1/f1, which gives i1 = 20.13 cm. Next, your calculation for o2 is also incorrect. The distance between the two lenses is 13 cm, so the object distance for lens 2 (o2) should be 13 cm, not -7.129 cm. Finally, your calculation for i2 is incorrect. The correct equation to use is 1/i2 = (1/f2) + (1/o2), which gives i2 = 4.05 cm.

To find the overall lateral magnification M, you can use the equation M = -i2/i1, which gives M = -0.201. This means that the final image produced by the system is inverted and smaller than the original object.

Remember to always double check your units and equations to avoid errors. Keep up the good work!