System focal length for thin lenses

[avelon]

Homework Statement

Three “thin” lenses, each with focal length 25 mm, are placed 5 cm from each other. What is system focal length?

Homework Equations

Lens equation: (1/o_xd) + (1/i_xd) = i/f_x
O_xd = object distance
I_xd = image distance
f_x = focal

The Attempt at a Solution

Lens1:
(1/o₁d) + (1/i₁d) = 1/f₁
(1/inf) + (1/i₁d) = 1/25
i₁d = 25 mm

Lens2:
O₂d = 50-25 = 25 mm
(1/o₂d) + (1/i₂d) = 1/f₂
(1/25) + (1/i₂d) = 1/25
i₂d = inf

Lens3:
O3d = inf
(1/o₃d) + (1/i₃d) = 1/f₃
(1/inf) + (1/i₃d) = 1/25
i₃d = 25

So if I draw a line from i3d to a line parallel to the optic axis (see attachment), I’ll get system focal length = 25 mm. Is this right?

 

[anathema]

Thank you for your question. Your approach is correct and your solution of 25 mm for the system focal length is also correct. The thin lenses are placed in a way that creates a parallel beam of light between them, so the image formed by the first lens becomes the object for the second lens, and so on. Therefore, the system focal length is equal to the focal length of each individual lens, which in this case is 25 mm. Your diagram is also a helpful way to visualize the setup. Good job! If you have any further questions, please do not hesitate to ask.



Scientist