Question

LIL
18. An object 2 cm tall is placed on the axis of a convex lens of focal length 5 cm at a distance of 10 m from the
optical centre of the lens. Find the nature, position and size of the image formed. Which case of image formation by convex lenses is illustrated by this example?​

Answer 1

Given:

• An object is tall = 2 cm
• The axis of a convex lens of focal length = 5 cm
• Distance of optical centre of the lens = 10 m

To Find:

• Find the nature,position and size of the image formed = ?
• Which case of image formation by convex lenses is illustrated by this example = ?

Solution:

Given,

• h1 = 2 cm
• f = 5 cm
• u = -10m = - 1000 cm

Using Formula:

$\sf \large \: \frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Now put the values

$\sf \implies \: \frac{1}{v} - \frac{1}{ - 1000} = \frac{1}{5} \\ \\ \sf \implies \: \frac{1}{v} = \frac{1}{5} - \frac{1}{1000} \\ \\ \sf \implies \frac{1}{v} = \frac{200 - 1}{1000} \\ \\ \sf \implies \: \frac{1}{v} = \frac{199}{1000} \\ \\ \sf \implies \: v = 5.02 \: cm$

Hence,the image is formed 5.02 cm behind the convex lens and is real and inverted.

As we know,

$\sf \: m = \frac{v}{u}$

Now put the values here

$\sf \implies \: m = \frac{5.02}{ - 1000} = - 0.005 \\ \\ \sf \implies m = \frac{h1}{h2} = - 0.005 \\ \\ \sf \implies \: \frac{h2}{2} = - 0.005\\ \\ \sf \implies \: h2 = - 0.1 \: cm$

Since, the object distance is much greater than the focal length,this example illustrated the case when the object is placed.