Question

A convex lenses forms a real image of an object magnified two times. The distance between the object and image is 60cm. Find the focal lenth of the lense

Answer 1

13.3cm ≈ 13cm

Step-by-step explanation:

The following data were obtained from the question:

Magnification (M) = 2

Distance between image and object = 60cm

Focal length (f) =..?

Next, we shall determine the image distance (v) and the object distance (u). This can be obtained as follow:

Magnification (M) = image distance (v) / object distance (u)

M = v/u

Magnification (M) = 2

2 = v/u

Cross multiply

v = 2u

From the question,

Distance between image and object = 60cm i.e

v + u = 60

v = 2u

2u + u = 60

3u = 60

Divide both side by 3

u = 60/3

u = 20cm.

v = 2u = 2 x 20 = 40cm

Now, we can obtain the focal length of the lens as follow:

1/f = 1/v + 1/u

u = 20cm.

v = 40cm

1/f = 1/v + 1/u

1/f = 1/40 + 1/20

1/f = (1 + 2)/40

1/f = 3/40

f = 40/3

f = 13.3cm ≈ 13cm

Therefore, the focal lenth of the lens is 13.3cm ≈ 13cm