Question

10cm tall image is projected on a screen 50cm away from the convex lens of focal length 20cm. Find the position and size of the object.

Answer 1

The focal length f =20cm

Height of image is 10cm,as it can be projected on screen so it is a real and inverted image.$\therefore$ according to sign conventions h'= -10cm

let height of object is h

As screen is 50cm away so the image distance v = 50cm

using lens formula

1/v - 1/u = 1/f

1/u = 1/v - 1/f

So, 1/u = 1/50 - 1/20

S0, 1/u = (2 - 5)/100

That is, 1/u = -3/100

So, u= -100/3 = -33.33

Thus, distance of object is 33.33 cm on the left side of lens.


Magnification of the lens

$m=\frac{h^{\prime }}{h}=\frac{v}{u}$

$h=h^{\prime }\times \frac{u}{v}$

put values: $h=(-10)\times \frac{(-33.33)}{50}=6.66cm$

hence, distance of object is 33.33cm on left and size of object is 6.66cm.