A lens system is formed with two identical converging lenses separated by 68.0 c

Question

A lens system is formed with two identical converging lenses separated by 68.0 cm. An object placed 25.0 cm in front of the first lens forms an upright image of a tree that is 1.50 m tall on a screen 1.07 m from the second lens. Determine a possible focal length of the lenses (identical means they are equal) as well as the size and orientation (upright or inverted) of the object needed to produce the required image for that focal length. (There are two possible solutions for the focal length, both converging.) Draw a ray diagram horizontally to scale for the first lens only. You may draw the vertical scale at whatever size is convenient for you. For full credit: Horizontal scale must be indicated on diagram. All rays must be drawn with a straight-edge. All three principle rays must be drawn even though only two are needed to locate the image. The focal point, center of curvature, object, and image must be positioned correctly or within a reasonable margin of error.

Explanation / Answer

lens 1:
u = -25cm
1/v - 1/u = 1/f
1/v + 1/25 = 1/f

now, u for lens 2 = d - v = 68 - v
v for lens 2 = 107 cm
f =f
so 1/107 - 1/(68 - v) = 1/f
1/107 - 1/(68 - v) = 1/v + 1/25
[- v - 39]25v = [25 + v]107*(68 - v)
-25 v^2 - 975v = 181900-2675v + 7276 v - 107v^2
82v^2 - 5576v - 181900 = 0
v = 92.0886 cm, -26.08866 cm

1/f = 1/v + 1/25 = 19.66 cm, 600.188 cm

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