Question

A concave mirror is used to focus the image of a flower on a nearby well, $120cm$ from the flower. If a lateral magnification of $16$ is desired, the distance of the flower from the mirror should be
$\begin{align}
  & A)8cm \\
 & B)12cm \\
 & C)80cm \\
 & D)120cm \\
\end{align}$

Answer 1

Hint: Magnification of a concave mirror is defined as the ratio of image distance to the object distance of the mirror. In the given question, image distance of the concave mirror is equal to the sum of object distance and an additional $120cm$. Combining both these pieces of information, we can arrive at the desired answer.

Formula used: $m=\dfrac{v}{u}$

Complete step by step answer:
We know that magnification of a concave mirror is defined as the ratio of image distance to the object distance of the mirror. Mathematically, magnification is given by
$m=\dfrac{v}{u}$
where
$m$ is the magnification of concave mirror
$v$ is the image distance from the concave mirror
$u$ is the object distance from the concave mirror
Let this be equation 1.
Coming to our question, we are given that magnification $(m)$ of the concave mirror is equal to $16$. Also, image distance of the concave mirror is given to be equal to the sum of object distance and an additional $120cm$. Therefore, we have
$v=u+120cm$
Let this be equation 2.
Now, substituting equation 2 in equation 1, we have
$m=\dfrac{v}{u}=\dfrac{u+120cm}{u}\Rightarrow m-1=\dfrac{120cm}{u}\Rightarrow 16-1=\dfrac{120cm}{u}\Rightarrow u=\dfrac{120cm}{15}=8cm$
Let this be equation 3.
Therefore, from equation 3, we can conclude that the object distance of the given concave mirror is $8cm$

So, the correct answer is “Option A”.

Note: Since the magnitude of magnification in the derived answer is positive, we can conclude that the image formed is virtual and erect. On the other hand, if the magnitude of magnification was negative, the image formed would have been real and inverted. Magnification is also given by the ratio of size of the image to the size of the object.