A concave shaving mirror has a focal length of 12.5 cm. if an upright pencil is placed 5.00 cm in front of the mirror

concave-shaving

#1

A concave shaving mirror has a focal length of 12.5 cm. if an upright pencil is placed 5.00 cm in front of the mirror, determine the magnification. Is the image virtual or real? Right side up or upside down?

Answer:

focal length of the concave mirror,f = 12.5 cm
Object is placed at 5 cm in front of the mirror

Now the radius of curvature would be 2f. Therefore, C=25 cm
The object is placed between the focal point and the vertex of the mirror.

Thus the image would be virtual, and right side up

Now to calculate magnification m = -[di/do]…(1)
here do = 5 cm
hence we need to find di

For that we would use the formula
1/di=(1/f)−(1/do)
which gives di as -8.33 cm. The negative here represents that the image is virtual in nature.

Now putting these values in (1)
now magnification, m =1.666