A single concave spherical mirror is used to create an image of a 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.If the image is 0.88 cm tall,what is the height of the source?

Question

Quizplus · Accepted Answer

Using the mirror formula 1/f = 1/do + 1/di, we can find the distance of the image from the mirror. We know that f = R/2 for a spherical mirror, where R is the radius of curvature. Substituting the given values, we get:
1/6 = 1/-23 + 1/di
Solving for di, we get: di = -7.99 cm (negative sign indicates that the image is formed on the same side as the object).
Using magnification formula m = -di/do, we can find the magnification of the image. Since the image is smaller than the object, the magnification is negative. Substituting the given values, we get:
-0.88/do = -7.99/23
Solving for do, we get: do = -5.69 cm (negative sign indicates that the object is to the left of the mirror).
The height of the source can be found using the magnification formula: m = hi/ho = -di/do. Substituting the given values, we get:
-0.88/ho = -7.99/5.69
Solving for ho, we get ho = 6.4 cm (rounded to one decimal place). Therefore, the answer is choice C, 6.4 cm.

A Single Concave Spherical Mirror Is Used to Create an Image