Answer to Question #178623 in Physics for Chaihcai

Question

REFLECTION AND MIRRORS

Show your solution and draw a ray of diagram.

3. A concave mirror has a focal length of 18 cm. Where will an image form if an object is placed 58 cm from the 

mirror? If the object is 12 cm tall, what will be the height of the image? Is the image erect or inverted? Real or virtual?

4. Where will the image form if the same object is placed 15 cm in front of a convex mirror with a focal length of 18

cm? (Hint: The focal length is behind the mirror.) How tall is the image? Is the image erect or inverted? Real or virtual?

Answer 1

3. Use concave mirror equation:

$$\frac{1}{f}=\frac{1}{o}+\frac{1}{i},\\\space\\ i=\frac{fo}{o-f}=26.1\text{ cm}.$$

Height of the image:

$$h_i=-\frac{i}{o}h_o=-\frac{26.1}{58}·12=-5.4\text{ cm}.$$

The image is real and inverted.

Diagram:

4. For our convex mirror, f=-18 cm, o=+15 cm, mirror equation:

$$i=\frac{fo}{o-f}=-8.2\text{ cm}.$$

Image height:

$$h_i-\frac{i}{o}h_o=-\frac{-8.2}{15}·12=6.5\text{ cm}.$$

The image is erect and virtual.