Question

A film projector magnifies a film of area 100 square centimeter on the screen. If linear magnification is 4 then area of magnified image on screen will be-
A. 1600 sq.cm
B. 800 sq.cm
C. 400 sq.cm
D. 200 sq.cm

Answer 1

Hint: Magnification is the process in which the object is observed in an enlarged size of the actual object. The real size of the object is smaller as compared to the image of the object. The exact opposite process of the magnification is known as de-magnification. In this process the image of the object is smaller than the size of the object.

Complete step by step answer:
Magnification is the process of enlargement of the object. Example: The bacteria observed from the microscope appears larger than its size. This magnification of the bacterial image is required to study its characteristics.
The linear magnification of the object is given as, ${{m}_{l}}=4$
The areal magnification of the object is given by,
$\Rightarrow {{m}_{a}}={{\left( {{m}_{l}} \right)}^{2}}$
Where, $m_a$ is the areal magnification
Substituting the given values in the above equation:
$\begin{align}
  & \Rightarrow {{m}_{a}}={{\left( 4 \right)}^{2}} \\
 & \Rightarrow {{m}_{a}}=16 \\
\end{align}$
Thus, the area after the magnification is given as:
$\begin{align}
  & \Rightarrow {{A}_{m}}={{m}_{a}}A \\
 & \Rightarrow {{A}_{m}}=16\times 100\ \text{sq}\text{.cm} \\
 & \Rightarrow {{A}_{m}}=1600\ \text{sq}\text{.cm} \\
\end{align}$
Correct option is A.

Note:
The linear magnification and the areal magnification are not similar. The linear magnification is one dimensional and the areal magnification is two dimensional. In the above question, you have to keep in mind that the areal expansion cannot be calculated directly from linear expansion.