Question

A slide projector gives a magnification of 10. If a slide of dimensions \[3{\text{ }}cm \times 2{\text{ }}cm\] is projected on the screen, the area of the image on the screen is:​
A) $6000\,c{m^2}$
B) $600\,c{m^2}$
C) $3600\,c{m^2}$
D) $12000\,c{m^2}$

Answer 1

Hint: The magnification in the slide projector will amplify the dimensions of the width of the length of the slide. The new area will be calculated using the magnified dimensions of length and breadth.

Formula used:
In this solution, we will use the following formula
Magnification: $m = \dfrac{{{h_i}}}{{{h_o}}}$ where ${h_i}$ is the image height and ${h_o}$ is the object height
Area of a rectangle $A = l \times b$ where $l$ is the length and $b$ is the breadth of the rectangle

Complete step by step solution:
We know that the magnification in terms of optics relates to the dimensions of the image and the object that is being enlarged. A slide projector enlarges both the dimensions of a rectangular slide film.
We’ve been given that a slide projector gives a magnification of 10. This implies that it will increase the dimensions of the slide by 10 times. Additionally, it will amplify both the dimensions of the slide.
So, the new dimensions of the image will be
${\text{Length = 3}} \times {\text{10 = 30}}\,{\text{cm}}$
And similarly, the breadth of the image will be
${\text{Breadth = 2}} \times {\text{10 = 20}}\,{\text{cm}}$
Hence the area of the image projected will be a product of the new length and breadth and can be calculated as
$A = 20 \times 30 = 600\,c{m^2}$

Thus, the area of the image on the screen will be $600\,c{m^2}$ hence the correct choice is option (B).

Note: We must be careful in determining the dimensions of the image since the slide projector will amplify both the dimensions of the slide and not any one of them. We don’t need to convert the dimension of the slide projector since the magnification is a dimensionless quantity and both the quantities only need to have the same units.