Two systems are formed from a converging lens and a diverging lens, as shown in
ID: 1792811 • Letter: T
Question
Two systems are formed from a converging lens and a diverging lens, as shown in parts a and b of the drawing. (The point labeled "Fconverging" is the focal point of the converging lens.) An object is placed inside the focal point of lens 1 at a distance of 12.81 cm to the left of lens 1. The focal lengths of the converging and diverging lenses are 15.00 and 20.0 cm respectively. The distance between the lenses is 50.0 cm. Determine the final image distance for each system, measured with respect to lens 2.
(a) di2 = ---Select--- (- or +) ---Select--- (cm, cm^-1, or no units) (b) di2 = ---Select--- (- or +) ---Select--- (cm, cm^-1, or no units)Explanation / Answer
focal length of converging lens f1 = 15 cm
focal length of diverging lens f2 = -20 cm
distance between two lenses d = 50 cm
a) object distance of convergong lens p = 12.81 cm
Thin lens equation is
1/ P + 1 / Q = 1 / f1
1/ Q = 1 / 15 - 1 / 12.81
image distance of converging lens is
Q = -87.739 cm
object distance of diverging lens P ' = d - Q
= 50 + 87.739 = 137.73
Thin lens equation is
1 / P' + 1 / Q' = 1 / f2
1 / 137.73+ 1 / Q' = -1 /20
Q' = -17.464 cm
b)
object distance of diverging lens p =12.81 cm
Thin lens equation is
1/ P + 1 / Q = -1 / 20
1/ Q = -1 / 20 - 1 / 12.81
object distance of diverging lens P ' = d - Q
= 50 + 7.80= 57.80cm
Thin lens equation is
1 / P' + 1 / Q' = 1 / f2
1 / 57.80+ 1 / Q' = 1 /15
Q' = 20.25 cm
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