Question

An object 50 cm tall is placed on the principal axis of a convex lens. Its 20 cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens.

Answer 1

Step 1, Given data

Height of the image, h' = -20 cm( Negative sign shows that the image is real and inverted)

Height of the object, h = 50 cm

Image distance, v = 10 cm

Step 2, Finding the focal length of the lens

We know,

m = $\frac{h^{\prime }}{h}$ = $\frac{v}{u}$

Or,

u = $\frac{v\times h}{h^{\prime }}$ = $\frac{10\times 50}{-20}$

After solving

u = -25 cm

From the lens formula

We know,

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

Putting all the values

$\frac{1}{f}$ = $\frac{1}{10}$ - $\frac{1}{-25}$ = $\frac{7}{50}$

Therefore, f = $\frac{50}{7}$

Hence the focal length, f = 7.14 cm