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An object of height 4.25 mm is placed at a distance of 10 cm from a convex lens of power +5D. Find (i) focal length of the lens, and (ii) size of the image.
Object height, $h$ = 4.25 mm = 0.425 cm $(\because 1cm=10mm)$
Object distance, $u$ = $-$10 cm
Power, $P$ = $+$5 D
To find: (i)Focal length $f$, (ii) Size of the image $h'$.
Solution: (i)
Power of the lens is given by-
$P=\frac {1}{f}$
Substituting the value of power, $P$ we get-
$5=\frac {1}{f}$
$f=\frac {1}{5}$
$f=+0.2m=20cm$
Thus, the focal length $f$ of the lens is 20cm.
Solution: (ii)
From the lens formula, we know that-
$\frac {1}{v}-\frac {1}{u}=\frac {1}{f}$
Substituting the given values we get-
$\frac {1}{v}-\frac {1}{(-10)}=\frac {1}{20}$
$\frac {1}{v}+\frac {1}{10}=\frac {1}{20}$
$\frac {1}{v}=\frac {1}{20}-\frac {1}{10}$
$\frac {1}{v}=\frac {1-2}{20}$
$\frac {1}{v}=-\frac {1}{20}$
$v=-20cm$
Thus, the distance of image $v$ is 20cm in front of the lens.
Now,
From the magnification formula, we know that-
$m=\frac {v}{u}=\frac {h'}{h}$
Sustituting the given value, we get-
$\frac {-20}{-10}=\frac {h'}{0.425}$
$2=\frac {h'}{0.425}$
$h'=2\times {0.425}$
$h'=+0.85cm=+8.5mm$
Thus, the size of the image $h'$ is 8.5cm, and the positive sign implies that the image is erect and virtual in nature.