Question

An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 35 cm beyond the first, this second lens having a focal length of 8.0 cm. If the height of the object is 6.0 cm6.0cm, what is the height of the final image?

A) 3.0 cm
B) 4.0 cm
C) 5.0 cm
D) 6.0 cm

Answer 1

The height of the final image is 6.0 cm.

Step-by-step explanation:

To find the height of the final image, we can use the thin-lens equation and the magnification formula. The thin-lens equation is given by: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the object distance, and di is the image distance. The magnification formula is given by: m = -di/do, where m is the magnification.

Using these formulas and the given information, we can calculate the image distance of the first lens to be 20 cm, and the image distance of the second lens to be 8 cm. Therefore, the total image distance from the object is 28 cm. Substituting this value into the magnification formula, we can find that the magnification is -2.33.

Now, using the magnification formula for the second lens, we can find that the height of the final image is -6 cm. However, since the height cannot be negative, we take the absolute value, resulting in a height of 6 cm.