Question

How far should an object be placed from a convex lens of focal length 20 cm to obtain its image at a distance of 30 cm from the lens? What will be the height of the image, if the objects is 6 cm tall?

Answer 1

Explanation:

Formula for image- object relationship:

                                                                    1/u+1/v=1/f

                                u is the object distance

                                 v is the image distance

                                  f is the focal length of the lens

If you know the focal length and object distance, using the above formula image distance can be calculated.

         1/u + 1/30 = 1/20

          1/u =  1/20 - 1/30

          1/u = 1/60

            u = 60 cm  so first ans is 60cm object should be placed at 60 cm from lens    

2nd part calculation for image height:

M= (image height)/(object height) = - (image distance)/(object distance)

         I/O = -ve(30/60)

          I/6 = -ve(1/2)

          I=  -3cm  here -ve sign shows that image in inverted

Answer 2

Explanation:

we know,

1/f=1/v - 1/u

and since it is a convex lens therefore f and v will be positive

therefore

1/20=1/30-1/u

1/u=1/30-1/20

1/u=(2-3)/60

1/u=-1/60

u=-60

linear maginfication

m=v/u

m=30/60

m=-1/2

in second case,

m=height of image/height of object

-1/2=height of image/6

height of image=-1/2×6

height of image=-3 cm.

- sign shows image is inverted.

therefore

height of image= 3cm