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 lens and image is $80cm$, at what distance should the candle be placed from the lens? What is the nature of the image at a distance of $80cm$ and the lens?

Answer 1

Step 1: Given

Magnification: $m=3$

Distance between convex lens and image: $v=80cm$

Distance between the object and convex lens is $u$

Step 2: Formula Used

Magnification of an image with respect to object is given by $m=\frac{v}{u}$. Thus, the distance between object and lens is $u=\frac{v}{m}$. And as per the sign convention, the distances between object and lens will be negative, therefore $u=-\frac{v}{m}$.

Step 3: Solution

Find the distance between the object and lens. Substitute the values in the formula.

$\begin{array}{rcl}u& =& -\frac{v}{m}\\ & =& -\frac{80}{3}cm\end{array}$

Since the image can be obtained on a screen, it is real and on the other side of the lens. This implies that the lens is a convex lens. And the image is real, inverted, and enlarged.

Ray diagram of a convex lens is,

Hence, the distance at which the candle should be placed from the lens is $-\frac{80}{3}cm$ and the image obtained is real, inverted, and enlarged.