Aaconverging lens of focal length 15 mm is used as a magnifying glass for inspecting stamp. A rectangular stamp which is 20mm 40mm is placed 30mm from the lens find the length of the image of the 20mm side of the stamp?

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Answer 1 · 2018-07-17T14:17:00

Lens formula is

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

Where

$object distance (u) = = - 30 m m$ $"object distance" (u)==-30mm$

$focal length (f) = + 15$ $"focal length" (f)=+15$

$image distance (v) = = ?$ $"image distance" (v)==?$

Now inserting in the eqution we get

$\frac{1}{v} - \frac{1}{- 30} = \frac{1}{15}$ $1/v-1/(-30)=1/15$

$\Rightarrow \frac{1}{v} = \frac{1}{15} - \frac{1}{30} = \frac{1}{30}$ $=>1/v=1/15-1/30=1/30$

$\Rightarrow v = 30 m m$ $=>v=30mm$

Hence magnification $(m) = \frac{v}{u} = \frac{30}{30} = 1$ $(m)=v/u=30/30=1$

So the image is real and the length of 20mm side of the stamp in the image will be same, 20mm.