A lens of focal length 20 cm is used to produce a ten times magnified image of a film slide on a screen. How far must the slide be placed from the lens?

Given:

Magnification, $m$ = $-$10 ($\because$ only a convex lens can form image on a screen, means the image will be real and inverted, and it is possible only when the magnification has a negative sign)

Focal length, $f$ = 20 cm

To find: Object (slide) distance, $u$ from the lens. 

 $-10=\frac {v}{u}$     

 $v=-10u$

Now,

According to the lens formula, we know that:

$\frac {1}{v}-\frac {1}{u}=\frac {1}{f}$

Substituting the value of $f$ and $v$ in the formula we get-

$\frac {1}{(-10u)}-\frac {1}{u}=\frac {1}{20}$

$-\frac {1}{10u}-\frac {1}{u}=\frac {1}{20}$

$\frac {1}{20}=\frac {-1-10}{10u}$

$\frac {1}{20}=\frac {-11}{10u}$

$10u=(-11)\times {20}$

$10u=-220$

$u=\frac {-220}{10}$

$u=-22cm$

Thus, the slide is placed at a distance of 22 cm from the poles of the lens.

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Updated on: 10-Oct-2022

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