Question

Which of the following will not produce a magnified image of an object?
A. Convex mirror
B. Concave mirror
C. Convex lens
D. Two convex lenses in contact

Answer 1

Hint:The magnification in case of mirrors is given as $m=-{\displaystyle \frac{v}{u}}$, whereas in case if lens, the magnification will be $m={\displaystyle \frac{v}{u}}$. If $m$ is positive, the image will be magnified and if $m$ is negative, the image will not be magnified.

Complete step by step answer:
First, let us consider a convex mirror. If the object is placed at infinity, the rays will hit the convex mirror and diverge. The rays appear to meet at the focus. A virtual image is formed. Here, the size of the image formed is negligible. The ray diagram is shown for the convex mirror when the object is kept at infinity.

If the object is placed at a finite distance: One ray will travel and hit the mirror perpendicularly so that it meets the center of curvature. Another ray will hit the mirror, diverge and then will meet at a point which is in between the pole and the focus of the convex mirror. In this case, a virtual image will be formed between the pole and the focus. The ray diagram is shown for the convex mirror when the object is kept at a finite distance.

As you can see, the height of the image is smaller than the height of the object. No matter where the object is placed, the image formed will always be smaller than the object.

Hence, convex mirrors will not produce a magnified image of an object.Option A is the correct answer.

Note: Here we got lucky to have the first option as the correct answer. What about the others? In case of a concave mirror, following cases will occur:
-When the object is kept at infinity, the image will form at the focus and the height of the image will be negligible.
-When the object is kept beyond the center of curvature, the image will form in between the focus and the center of curvature and the size of the image will be smaller than the size of the object.
-When the object is kept at the center of curvature, the image will form at the same point and the size of the image will be equal to the size of the object.
-When the object is kept in between the center of curvature and the focus, the image will form behind the center of curvature and the size of the image will be enlarged.
-When the object is kept at the focus, the image will form at infinity and the size will be enlarged.
By applying similar analysis, you can check for the rest of the option. The image produced will be magnified.