Answer to Question #181574 in Optics for anuj

Question

object is placed in front of a diverging lens with a focal length of 8 CM. Find the image distance for an object distance of 12 cm. Answer in units of cm.

Answer 1

Solution. The lens equation expresses the quantitative relationship between the object distance (d_o), the image distance (d_i), and the focal length (F). For a diverging lens, we write the equation as

$$-\frac{1}{F}=\frac{1}{d_0}-\frac{1}{d_i}.$$

According to the condition of the problem F=0.08m, d_o=0.12m. Hence

$$\frac{1}{d_i}=\frac{1}{d_0}+\frac{1}{F}$$

$$d_i=\frac{d_0\times F}{d_0+F}=\frac{0.08\times 0.12}{0.08+0.12}=0.048m=4.8cm$$

Answer.

$$d_i=4.8cm$$