Question

The image of a candle flame placed at a distance 36 cm from a spherical lens is formed on a screen placed at a distance of 72 cm from the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 2.5 cm, find the height of its image.

Answer 1

u=-36 cm
v =72 cm
h=2.5 cm
Using lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\frac{1}{f}=\frac{1}{72}-\frac{1}{(-36)}=\frac{1}{72}+\frac{1}{36}=\frac{1+2}{72}=\frac{3}{60}=\frac{1}{20}f=+20cm$
Positive focal length represents convex lens,
Now,
$m=\frac{v}{u}=\frac{h^{\prime }}{h}\Rightarrow \frac{72}{-36}=\frac{h^{\prime }}{2.5}{h}^{\prime }=\frac{-72}{36}\times 2.5h^{\prime }=-5.0cm$