# A concave lens has focal length of 20 cm. At what distance from the lens a 5 cm tall object be placed so that it forms an image

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A concave lens has focal length of 20 cm. At what distance from the lens a 5 cm tall object be placed so that it forms an image at 15 cm from the lens? Also calculate the size of the image formed.

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According to the question;

Object distance = u;

Image distance (v) = -15cm;

Focal length = -20cm

By lens formula;

$\frac1v-\frac1u=\frac1f$

⇒ $\frac1{15}-\frac1u=\frac1{-20}$

⇒ $\frac1{u}=\frac1{20}-\frac1{15}$

⇒ $\frac1{u}=\frac{3-4}{60}=\frac{-1}{60}$

⇒ u = -60cm.

Therefore, object is placed at 60 cm in front of lens.

Now;

Height of object h1= 5cm;

Magnification = $\frac{h_2}{h_1}=\frac{v}{u}$

Putting values of v and u

Magnification = $\frac{h_2}{5}=\frac{-15}{-60}$

⇒ $\frac{h_2}{5}=\frac{1}{4};$

⇒ h2$\frac54$ = 1.25

Height of image is 1.25 cm.

Positive sign means image is virtual.