Question

You look at yourself in a shiny 8.8-cm-diameter Christmas tree ball.

If your face is 29.0 cm away from the ball's front surface, where is your image? Follow the sign conventions. Express your answer to two significant figures and include the appropriate units.

Answer 1

When looking at yourself in a shiny Christmas tree ball, your image is located 127.1 cm behind the ball's surface.

Step-by-step explanation:

To determine where your image is located when you look at yourself in the shiny Christmas tree ball, we can use the mirror formula:

1/f = 1/do + 1/di

Using the given information, the radius of the ball is 8.8 cm (which means the diameter is 17.6 cm) and your face is 29.0 cm away from the ball's front surface.

Plugging in the values into the formula:

1/f = 1/29.0 cm + 1/di

Where f is the focal length and di is the distance of the image.

Since the radius of the Christmas tree ball is 8.8 cm, the focal length is half the radius, which is 4.4 cm.

1/4.4 cm = 1/29.0 cm + 1/di

Solving for di we find:

di = -127.1 cm

So your image would be located 127.1 cm behind the ball's surface.