Physics and Images Problem

Question

A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Detemine the image distance and the image size.

Answer 1

Using the physics optics equations we can find image distance and height.

1/f = 1/d_o + 1/d_i where f=focal length, d_o= object distance, d_i= image distance

so with your example to find first the image distance (we will use this to find image size) plug in the given values. It is ok to leave units in cm as long as your are consistent.

1/15.2 = 1/45.7 + 1/d_i

Then using the magnification equation M= h_i/h_o = -d_i/d_o you can plug in the object height (h_o) given in the question stem and the value for image distance that you found in the first part as well as the same object distance and then solve for your unknown, h_i.

Answer 2

The above equations are the mirror equation and and Magnification equation. In this equation f denotes the focal length, d_o denotes the distance length from the mirror, i_o denotes the distance of the image from the mirror, h_i denotes the height of the image, h_o denotes the height of the object, and M denotes the magnification.

To solve the problem, we will substitute in what we know. The information we know is as follows:

h_o = 4.00 cm

d_o = 45.7 cm

f = 15.2 cm

We are asked to find the d_i and the h_i.

1/f = 1/do + 1/d_i1/(15.2 cm) = 1/(45.7 cm) + 1/d_i

0.0658 cm^-1 = 0.0219 cm^-1 + 1/d_i

0.0439 cm^-1 = 1/d_i

d_{i =} 22. 8 cm

h_i/h_o = - d_i/d_oh_i /(4.0 cm) = - (22.8 cm)/(45.7 cm)

h_i = - (4.0 cm) • (22.8 cm)/(45.7 cm)

hi = -1.99 cm

The negative sign indicates the image is in inverted.