Question

You have two lenses A and B of focal lengths +10 cm and –10 cm, respectively. State the nature and power of each lens. Which of the two lenses will form a virtual and magnified image of an object placed 8 cm from the lens? Draw a ray diagram to justify your answer

Answer 1

Given: Focal length of lens A, f_A = +10 cm = +0.1 m

Focal length of lens B, F_B = −10 cm = −0.1 m

To calculate the power of lens A:-

The power of lens A, P = 1/F_A(in metres)

P = 1/ +0.1

∴ P = +10 dioptre or +10 D

The positive sign indicates that it is a converging or convex lens.

To calculate the power of lens B:-

The power of lens B, P = 1/F_B(in meters)

P = 1/ -0.1

∴ P = −10 dioptre or −10 D

The negative sign indicates that it is a diverging or concave lens.

In a convex lens, when the object is placed between the pole and focus, the image formed is always virtual and magnified. On the other hand, a concave lens produces a virtual, erect but diminished image.

Here the object is placed 8 cm from the lens which is at a distance less than the focal length, i.e. less than 10 cm. Thus, the 8 cm position of the object placed in front of the convex lens will produce a virtual and magnified image. The diagram for the same is as shown below: