Question

An object 4 cm high is placed 15 cm from a convex lens of focal length 5 cm draw a ray diagram on graph paper and find its position, size and nature of the image

Answer 1

Answer:

Explanation:

Object distance given is 15cm which is (u).

Object length(o) = 4 cm.

Focal length(f) = 5 cm.

Thus, magnification(m) is object distance / image distance

m=i/o.

Or, we can say -

1/v - 1/u=1/f

1/v - 1/15 = 1/5

So, 1/v = 1/5 + 1/15

        1/v = 4/15

          v= 15/4 cm which is the position of the image from the                 convex lense.

Thus, magnification is (f-v)/f=m

                                 =(5-15/4)/5=m

                                 = 5/20=m

                                  m=1/4.

Now, m=i/o for all lenses  

=1/4=image / 4

So, image distance is 1 cm.

Nature of the image will be larger and inverted.

Answer 2

object's height, $h_0$ = 4cm

object distance , u = -15cm

focal length of convex lens , f = +5cm

using lens maker formula,

1/v - 1/u = 1/f

or, 1/v - 1/-15 = 1/5

or, 1/v = 1/5 - 1/15 = 2/15

or, v = 15/2 = +7.5 cm

as image distance is positive, image is real and it is located at 7.5cm behind the lens ( right side).

magnification, m = v/u = height of image /height of object.

or, (+7.5)/(-15cm) = height of image/(4cm)

or, height of image = -2cm < height of object

hence, image is real and diminished.

see diagram , which shows image position, nature and size.