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# Define power of a lens. What is its unit? One student uses a lens of focal length 50 cm and another of -50 cm. What is the nature of the lens and its power used by each of them?

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:**The focal length of lens A, $f_A=+50\ cm$

$=0.5\ m$ [converted 'cm' into 'm']

Focal length of lens B, $f_B=-50\ cm$

$=-0.5\ m$ [converted 'cm' into 'm']

**To find:**Nature and power of each lens $(A\ and\ B)$.

**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-

$P=\frac{1}{0.5}$

$P=+2\ D$

Thus, the power of lens A is $2\ D$, 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-

$P=\frac{1}{-0.5}$

$=-2\ D$

Thus, the power of lens A is $-2\ D$, and the minus sign implies that it is diverging or concave in nature.

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