Question

An object when placed in front of a convex lens forms a real image of 0.5 magnification . If the distance of the image from the lens is 24 cm , Calculate focal length of the lens .

Answer 1

It is given that image distance [v] = 24 cm.

The magnification  [m] = 0.5

As per the rule of sign convention for lens, the measurement taken opposite to the direction of light is taken as  negative.

As the image is real, so the image must be formed on the other side of the lens .

Hence, v = +24 cm

As the image is real, so the magnification is taken as negative.

Hence, m = -0.5

We are asked to calculate the focal length [f] of the lens.

The magnification in terms of v and f is given as -

                                 $m=\frac{f-v}{f}$

                              ⇒   $mf=f-v$

                               ⇒  $f\ = \frac{v}{1-m}$

                                        $=\frac{(24)}{1-(-0.5)}$

                                        $=16\ cm$

Hence, the focal length of the convex lens is 16 cm.

Answer 2

Answer:

V=24

m=0.5

m=-v/u

m=48

1/f=1/u+1/v

1/f=1/-48+1/24

1/f=1/24

Hence focal length=24