Answer to Question #149310 in Optics for Gwen

Question

Lens Equation

Solve the following problems.

1.An object 8 cm tall is placed 30 cm from a converging lens. A real image is

formed 15 cm from the lens. (5 pts.)

          a. What is the focal length of the lens?

          b. What is the size of the image?

          c. Describe the image using the ray diagram.

2.A diverging lens has a focal length of 2.5 cm. If it is placed 4 cm from an object, at

what distance from the lens will the image be located? Describe the image. (3pts.)

Answer 1

1)

a)

$$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}=\frac{1}{30}+\frac{1}{15}\\f=10\ cm$$

b)

$$\frac{d_i}{d_o}=-\frac{h_i}{h_o}\\\frac{0.15}{3}=-\frac{h_i}{0.08}\\h_i=-0.04\ m=-4\ cm$$

c)

Real, diminished, real.

2)

$$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}\\\frac{1}{-2.5}=\frac{1}{4}+\frac{1}{d_o}\\d_o=-1.54\ cm$$