What is meant by power of a lens? Define its SI unit. 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.

Academic Physics NCERT Class 10

The 'power of a lens, $P$ is defined as, the ability of a lens to converge or diverge a beam of light falling on it. Also, it is the reciprocal of its focal length.

That is, $P=\frac {1}{f}$

The S.I unit of power of lens is dioptre, which is denoted by $D$.

Given:

Focal length of lens A, $f_A=+10cm=+0.1m$ (converted 'm' into 'km')

Focal length of lens B, $f_b=-10cm=-0.1m$ (converted 'm' into 'km')

To find: Nature and power of each lens (A & B).

Solution:

To calculate the power of the lens A.

We know that power of the lens is given as-

$P=\frac {1}{f}$

Putting the value of $f_A$ in the above expression we get-

$P=\frac {1}{0.1}$

$P=\frac {10}{1}$

$P=+10D$

Thus, the power of lens A is 10D, and the plus sign implies that it is converging or convex in nature.

Now,

To calculate the power of the lens B.

We know that power of the lens is given as-

$P=\frac {1}{f}$

Putting the value of $f_B$ in the above expression we get-

$P=\frac {1}{-0.1}$

$P=-\frac {10}{1}$

$P=-10D$

Thus, the power of lens A is 10D, and the minus sign implies that it is diverging or concave in nature.

In a convex lens when the object is placed within the focus $(F')$, or between the optical centre, $(C)$ and focus $(F')$, the image formed is always virtual, erect, and magnified. While, a concave lens produces virtual, erect but diminished image regardless of the distance of the object from the lens.

Here, the object is placed 8cm from the lens which is at a distance less than the focal length. Thus, in this case, the convex lens will produce a virtual and magnified image of the object.

The diagram showing this case is given below:-

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Updated on: 10-Oct-2022

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