Answer to Question #162592 in Optics for Eva

Question

An object is located 50.0cm from a converging lens having a focal length of 15.0cm. Which of the following statements is true regarding the image formed by the lens?

A. It is virtual, upright, and larger than the object

B. It is real, inverted, and smaller than the object.

C. It is virtual, inverted, and smaller than the object.

D. It is real, inverted, and larger than the object.

Answer 1

Let's first find the image distance from the lens equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$d_i=\dfrac{1}{\dfrac{1}{f}-\dfrac{1}{d_o}}=\dfrac{1}{\dfrac{1}{15\ cm}-\dfrac{1}{50\ cm}}=21.43\ cm.$$

The sign plus means that the image is real.

Let's find the magnification of the image:

$$M=\dfrac{-d_i}{d_o}=\dfrac{-21.43\ cm}{50\ cm}=-0.43.$$

The sign minus means that the image is inverted. Also, the image is smaller than the object.

Thus, the image is real, inverted, and smaller than the object. Hence, the correct answer is (B).

Answer:

B. It is real, inverted, and smaller than the object.