Question

The image of a person appears inverted on the far side of an optical instrument. Identify the optical instrument?
(A) Concave mirror
(B) Convex mirror
(C) Plane mirror
(D) Concave lens
(E) Convex lens

Answer 1

Hint
For solving this question, we need to figure out which optical instrument can make the light rays meet on the far side after passing through it. At the same time, we need to check that the image formed is inverted.

Complete step by step answer
Both the concave and convex mirrors reflect the incident light rays of the object which is placed in front of it. So, the image is produced on the same side of the object. So, both the concave and convex cannot produce the image on the far side of them.
Therefore, options A and B are incorrect.
A plane mirror forms an image on the far side, but the image is not inverted. It is erect.
Therefore, option C is also incorrect.
A concave lens diverges the incident rays of light of the object placed in front of it. So a concave lens produces the image on the same side of the object. Thus, a concave lens also cannot produce the image on the far side.
Therefore, D is also incorrect.
A convex lens converges the light rays incident on it. So, it produces the image on the far side.
Now, the magnification formula for a lens is given by the expression
$m = \dfrac{v}{u}$, where $v =$image distance,$u =$object distance.
Since the object and image are on opposite sides of the convex lens, so $v$and $u$have opposite signs.
From the magnification formula above, we see that the ratio of values of opposite signs is negative. Thus the magnification is negative. This means that the image formed is negative.
So, an inverted image is produced on the far side of the convex lens.
Hence, the correct answer is option E, convex lens.

Note
For the concave mirror, there is a case when the image is produced on its far side. This is when the object is placed between the principal focus and the pole of the mirror. But the image formed is not inverted, but is erect. So, don’t get confused by this special case of the concave mirror.