Question

An object is 10 cm in front of a concave mirror which produces an upright image. The radius of curvature of the mirror is:
(A) 20 cm
(B) More than 20 cm
(C) Less than 10 cm
(D) Between 10 cm to 20 cm

Answer 1

In order to this question we will apply the mirror formula and with help of the magnification and nature by the analysis of this we can find the radius of curvature of the mirror and for this we need to have the knowledge of the formation of image erect in the approximate position.

Complete step by step solution:
For solving this question we need to have the knowledge of image formation in different positions so starting from the first when we place the object at its focus of the concave mirror the image will form at infinity and it is real, inverted and highly enlarged.
Now we will see it for the object is placed between the center and focus of the concave mirror the image will be formed beyond C real and inverted and will be highly enlarged.
For the object placed at the center of curvature C the image formed will be at the center of curvature of the same size real and inverted.
Now for the object placed beyond the center of curvature the image formed will be between the focus and the center of curvature, diminished and of real and inverted nature.
At last if we place the object at the infinity the formation of image will be at the focus F highly diminished and real and inverted.
An erect image is formed by the concave mirror when the object distance is smaller than the focal length of the mirror. In this case, the object is 10 cm in front of a concave mirror which produces an upright image. So, the focal length must be greater than 10 cm.
We know that the radius of curvature is twice the focal length.

Note:
By changing the position of the object from the concave mirror, different types of images can be formed. Different types of images are formed when the object is placed:
At infinity, beyond the center of curvature, at the center of curvature, between the center of curvature and principal focus, at the principal focus and between the principal focus and pole. But in case of the convex mirror there are only two positions which are at the finite distance and at the infinite distance.