Question

An object 20 cm tall is placed on the principal axis of a convex lens . its 30 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

hope it will help you

Answer 2

Concept

Lens equation or lens formula is an equation that relates the focal length, image distance, and object distance for a spherical mirror. It is given as,

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

where.

v = Distance of the image from the lens.

u = Distance of the object from the lens.

f = Focal length of the lens.

Given

We have given the height of the object $h_0=20cm$ and the distance of the image from the lens(v) = 10cm and the height of the image $h_I= 30cm$

Find

We are asked to determine the focal length of the lens.

Solution

Magnification of conex lens is given by

$m=\frac{h_I}{h_0} =\frac{v}{u} \\\frac{-30}{20} =\frac{10}{u}$

On cross multiplying, we get

$u=-\frac{20}{3}$

Putting $u=-\frac{20}{3} , \ v=10$  in thin lens formula

Thin lens formula  is given by

$\frac{1}{f} =\frac{1}{v} -\frac{1}{u}\\\\\frac{1}{f}=\frac{1}{10} +\frac{3}{20}\\\\\frac{1}{f}=\frac{2+3}{20}\\\\ \frac{1}{f}=\frac{5}{20}$

On reciprocal , we get

$f=4cm$

Therefore, the focal length of the lens is 4cm .

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