Question

A ray diagram can be used to find the location of an object if you are given the location of its image and the focal length of the mirror.

Part A

Draw a ray diagram to find the height and position of an object that makes a 1.7-cm-high upright virtual image that appears 8.0 cm behind a convex mirror of focal length 25 cm .

Express your answer using two significant figures.

p=

Part B

Express your answer using two significant figures.

h=

Answer 1

Given:-

di = 8.0 cm, f = 25 cm , hi = 1.7 cm

The sign conventions for the given quantities in the mirror equation and magnification equations are as follows:

• f is + if the mirror is a concave mirror

• f is - if the mirror is a convex mirror

• di is + if the image is a real image and located on the object's side of the mirror.

• di is - if the image is a virtual image and located behind the mirror.

• hi is + if the image is an upright image (and therefore, also virtual)

• hi is - if the image an inverted image (and therefore, also real)

a) To determine the object distance (di), the mirror equation will have to be used. The following lines represent the solution to the object distance; substitutions and algebraic steps are shown.

1/f = 1/do + 1/di

1/(-25 cm) = 1/do + 1/(-8 cm)

-0.04 cm^-1 = - 0.125 cm^-1 + 1/do

0.085 cm^-1= 1/do

do = 11.76 cm

b) To determine the object height (hi), the magnification equation is needed. Since three of the four quantities in the equation (disregarding the M) are known, the fourth quantity can be calculated. The solution is shown below.

hi/ho = - di/do

(1.7 cm)/ho = - (-8 cm)/(11.76 cm)

ho = (1.7 cm) • (11.76 cm)/(8 cm)

ho = 2.50

Mirror plane Object Image 11.76 am 8 cm 25 cm