Question

You are looking for a mirror so that you can see a four-fold magnified virtual image of an object when the object is placed 5 cm from the vertex of the mirror. What kind of mirror do you need? What should be the radius of curvature of the mirror?

a. Concave mirror with a radius of curvature of 5 cm
b. Convex mirror with a radius of curvature of 15 cm
c. Concave mirror with a radius of curvature of 10 cm
d. Convex mirror with a radius of curvature of 10 cm

Answer 1

To see a four-fold magnified virtual image of an object, a convex mirror is needed. The radius of curvature of the mirror should be -20 cm.

Step-by-step explanation:

To see a four-fold magnified virtual image of an object, you need a convex mirror. The formula for calculating the magnification of an image for a mirror is given by: m = -di/do, where m is the magnification, di is the image distance, and do is the object distance. In this case, the object distance is given as 5 cm.

So, the magnification equation becomes 4 = -di/5. Solving for di, we get di = -20 cm. Since the image is virtual, the negative sign indicates that it is on the same side as the object. Therefore, the image is 20 cm behind the mirror.

The radius of curvature of a convex mirror is always positive and equal to twice the focal length. Since the image is virtual, the focal length is negative. So, the focal length is -10 cm and the radius of curvature is -20 cm.