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The below image shows a thin lens of focal length 5 m.
(i) What is the kind of lens shown in the above figure?
(ii) If a real inverted image is to be formed by this lens at a distance of 7 m from the optical centre, then show with calculation where should the object be placed?
(iii) Draw a neatly labelled diagram of the image formation mentioned in (ii).

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(i) Convex lens

(ii) Given,

Image distance (v) = 7 m

Focal length (f) = 5 m

Object distance (u) = ?

Using formula,

$\dfrac{1}{\text{f}}$ = $\dfrac{1}{\text{v}}$ - $\dfrac{1}{\text{u}}$

We get,

$\dfrac{1}{\text{5}}$ = $\dfrac{1}{\text{7}}$ - $\dfrac{1}{\text{u}}$

$\dfrac{1}{\text{u}}$ = $\dfrac{1}{\text{7}}$ - $\dfrac{1}{\text{5}}$ = $\dfrac{5-7}{\text{35}}$ = $\dfrac{-2}{\text{35}}$

So, u = - $\dfrac{35}{\text{2}}$ = -17.5 m

Hence, object should be placed at 17.5 m on the left side of the convex lens.

(iii) Below ray diagram shows the image formation:

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