Question

The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between the lens and image is 80 cm, at what distance should the candle be placed from the lens? What is the nature of the image at a distance of 80 cm and the lens?

Answer 1

Step 1: Given Data
$Sizeofimageofflame=3\times sizeofflame$
$$\begin{gathered} Imagedis\tan ce\left(v\right)=80cm \\ Objectdis\tan ce=u\left(Assume\right) \end{gathered}$$

Step 2: Calculating the distance of the candle from the lens
As the image is obtained on the screen, so it is real in nature. Since the image formed is real, it will be inverted.
The magnification of an inverted image is negative.
So it can be written as:
$Magnification\left(m\right)=–3$

From the formula of magnification, we have:

$$\begin{gathered} m=\frac{v}{u} \\ \Rightarrow -3=\frac{80}{u} \\ \Rightarrow u=-\frac{80}{3}=-26.67cm(-vesignindicatesthattheobjectistotheleftoflens) \end{gathered}$$
Thus, the candle should be placed at a distance of $26.67cm$ to the left of the lens in order to have an image that is three times the size of the flame and the nature of the image formed is real and inverted.