Question

#1 #2 #1 #2 Object Object Fconverging converging

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 6.4 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 is 50.0 cm. Determine the final image distance for each system, measured with respect to lens 2

Answer 1

a) The focal length of lens #1 is f1 = 15.00 cm, and the object distance is do1 = 6.4 cm.

1/di1 = 1/f1 -1/do1 = 1/15 - 1/6.4
di1 = -11.1628 cm

This image is located to the left of lens #1 and serves as the object for lens #2. Thus, the object distance for lens #2 is di2 = 11.1628 cm + 50.0 cm = 61.1628 cm.
1/di2 = 1/f2 - 1/do2 = 1/-20 -1/61.1628
di2 = -15.0716 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 = –20.0 cm, and the object distance is do1 = 6.4 cm
1/di1 = 1/f1 -1/do1 = 1/-20 - 1/6.4
di1 = -4.84848

This image is located to the left of lens #1 and serves as the object for lens #2. Thus the object distance for lens #2 is
di2 = 4.84848 cm + 50.0 cm = 54.84848 cm.

1/di2 = 1/f2 - 1/do2 = 1/15 - 1/54.84848
di2 = 20.6464 cm

The positive value for di2 indicates that, as expected, the final image is to the right of lens #2.