Question

a convex lens of power 4d is placed at a distance 40cm from a wall.At what distance from the lens should a candle be placed so that image formed on the wall?​

Answer 1

GivEn :

• Power, P = 4D

• Image distance, v = 40 cm

To find :

Distance from the lens should a candle be placed so that image formed on the wall.

Solution :

As we're given with the Power and the image distance, we'll calculate the focal length of the convex lens at first.

=> Focal length = 1/P

=> Focal length = 1/4

=> Focal length = 0.25 m

or

=> Focal length = 25 cm

Now, we'll calculate the object distance, that is, the value of (v).

By using the LENS formula :

$:\implies \sf \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

$:\implies \sf \dfrac{1}{u} = \dfrac{1}{v} - \dfrac{1}{f}$

$:\implies \sf \dfrac{1}{u} = \dfrac{1}{40} - \dfrac{1}{25}$

$:\implies \sf \dfrac{1}{u} = \dfrac{5 - 8}{200}$

$:\implies \sf \dfrac{1}{u} = \dfrac{ - 3}{200}$

$:\implies \sf {u} = \dfrac{ - 200}{3}$

$:\implies \sf { \boxed{ \blue{ \frak{{u} = - 66.67 \: cm}}}} \: \: \bigstar$

$\therefore$The candle should be placed at a distance of 66.67 cm from the lens to form an image on the wall.