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

Answer 1

$$\textbf{Step 1 - Calculating position of candle}$$

Since image is $$3$$ times the size of object

$$\Rightarrow \text{ Magnification }(m) = -3$$

Using magnification formula,

$$m = \dfrac {v}{u}$$

$$\Rightarrow -3 = \dfrac {80}{u}$$

$$\Rightarrow u = \dfrac {-80}{3} cm$$

$$\textbf{Step 2 - Calculating forcal length}$$

Using Lens formula,

$$\dfrac {1}{f} = \dfrac {1}{v} - \dfrac {1}{u}$$

$$\Rightarrow \dfrac {1}{f} = \dfrac {1}{80} + \dfrac {3}{80}$$

$$\Rightarrow f = 20\ cm$$

$$\textbf{Step 3 - Nature of image and lens}$$

$$\bullet$$ Image is formed on other side of lens

hence it a real and inverted image.

$$\bullet$$ Focal length is positive, so lens is convex.