A single concave spherical mirror is used to create an image of a 6.00-cm tall source.The source is located 23.0 cm to the left of the mirror's center of curvature.The magnitude of the radius of curvature for the mirror is 12.0 cm.Calculate the magnification.

Question

Quizplus · Accepted Answer

Using the mirror equation:
1/f = 1/Do + 1/Di
where f is the focal length, Do is the object distance, and Di is the image distance
We know:
f = R/2 = 6.00 cm
Do = -23.0 cm (negative because it is to the left of the mirror)
Solving for Di:
1/Di = 1/f - 1/Do
1/Di = 1/6 - 1/-23
Di = -0.857 cm (negative because it is behind the mirror)
Using the magnification equation:
m = -Di/Do
m = -(-0.857 cm)/(23.0 cm)
m = 0.037 or -0.21 (rounded to two decimal places)
Since the object is upright and the image is inverted, the magnification is negative. Therefore, the best choice is C, -0.21.

A Single Concave Spherical Mirror Is Used to Create an Image