Two systems are formed from a converging lens and a diverging lens, as shown in
ID: 1298397 • 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 7.70 cm to the left of lens 1. The focal lengths of the converging and diverging lenses are 15.0 and -20.0 cm respectively. The distance between the lenses is50.0 cm. Determine the final image distance for each system, measured with respect to lens 2.
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 7.70 cm to the left of lens 1. The focal lengths of the converging and diverging lenses are 15.0 and -20.0 cm respectively. The distance between the lenses is50.0 cm. Determine the final image distance for each system, measured with respect to lens 2.Explanation / Answer
a) The focal length of lens #1 is f1 = 15.00 cm, and the object distance is 7.7 cm
1/f1 = 1/do + 1/di
1/di = 1/f - 1/do = 1/15 - 1/7.7
di = -15.822 cm
This image is located to the left of lens 1 and serves as the object for lens2. Thus, the object distance for lens 2 is di2 = 15.822 cm + 50.0 cm = 65.822 cm.
1/f2 = 1/do2 + 1/di2
1/di2 = 1/f2 - 1/do2 = 1/-20 - 1/65.822
di2 = -15.34 cm
The negative value for di2 indicates that, as expected, the final image is to the left of lens 2.
b) The focal length of the lens #1 is f1 =
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