Question

An object 2cm tall is kept on the principal axis of a converging lens of focal length 8cm. Find the position, nature and size of the image formed if the object is at 12cm from the lens. Also find the magnification produced by the lens. .

Answer 1

*Converging lens are also known as convex lens

Object distance (u) = -12 cm (negative)

focal length (f) = -8 cm (negative)

Height of the object (h) = 2 cm

By using lens formula

$\mathtt{\implies\:\frac{1}{f} = \frac{1}{v} - \frac{1}{u}}$

$\mathtt{\implies\:\frac{1}{v} = \frac{1}{f} + \frac{1}{u}}$

$\mathtt{\implies\:\frac{1}{v} = \frac{1}{-8} + \frac{1}{-12}}$

$\mathtt{\implies\:\frac{1}{v} = \frac{-3 - 2}{24}}$

$\mathtt{\implies\:\frac{1}{v} = \frac{-5}{24}}$

$\mathtt{\implies\: v = \frac{-24}{5}}$

$\mathtt{\implies\: v = -4.8 cm}$

$\mathtt{magnification (m) = \frac{v}{u}}$

$\mathtt{\implies\: \frac{-4.8}{-12}}$

$\mathtt{\implies\: + 0.4}$

we also know that

$\mathtt{magnification (m) = \frac{h'}{h}}$

$\text{ where, h' = height of the image}$

$\mathtt{\implies\: 0.4 = \frac{h'}{2}}$

$\mathtt{\implies\: h' = 0.8}$

*The image formed is diminshed, real, inverted and 4.8 cm infront of the mirror