A student-focussed the image of a candle flame on a white screen using a convex lens. He noted the position of the candle, lens, and screen as 12 cm, 50 cm, and 88 cm respectively. What is the focal length of the convex lens?

Object distance, u = position of the lens - position of the candle
=> u = 50 - 12

=> u = 38 cm

The image distance, v = position of the screen - position of the lens

=> v = 88 - 50

=> v = 38 cm
Applying the sign convention,

$\mathrm{u}=-38 \mathrm{cm}; \mathrm{v}=38 \mathrm{cm}$
Using the lens formula,

$\Rightarrow \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}$
$\Rightarrow \frac{1}{\mathrm{f}}=\frac{1}{38}-\frac{1}{-38}$

$\Rightarrow \frac{1}{\mathrm{f}}=\frac{1}{38}+\frac{1}{38}$
$\Rightarrow \mathrm{f}=19 \mathrm{cm}$
Hence, the focal length of the lens is f = 19 cm.