Question

The focal length of a convex lens is 10 cm. An object is placed at a distance of 20 cm from the lens. The image formed at
a. 10 cm
b. 40 cm
c. 30 cm
d. 20 cm​

Answer 1

$\huge \rm {Answer:-}$

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★This simple question is based on a simple formula ,

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

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$\sf \red {\underline{Given:-}}$

★The focal length(f) of a convex lens is 10 cm.

★Distance of the object at which it is placed(u)=20

★Distance of the object is often considered as negative for both concave and convex mirrors.

★Hence,u=-20

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$\sf \blue {\underline{To\: Find:-}}$

★Distance of the image formed (v)=?

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$\sf \pink {\underline{Using\: the\: formula:-}}$

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

f=focal length.

u=object distance (negative)

v=image distance

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$\sf \purple {\underline{Supplanting\: the\: values,}}$

$\large \mapsto {\frac{1}{10}=\frac{1}{v}-\frac{1}{(-20)}}$

$\large \mapsto {\frac{1}{v}=\frac{1}{10}-\frac{1}{20}}$

$\large \mapsto {\frac{1}{v}=\frac{2-1}{20}}$

$\large \mapsto {\frac{1}{v}=\frac{1}{20}}$

$\large \mapsto \green {\fbox{v=20cm}}$

★Distance of the image formed (v)=20cm

★Hence,"Option D is the correct answer "

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$\sf \orange {\underline{Info:}}$

★Object distance (u) for a concave mirror or convex mirror is always negative because an object is always placed to the left side of the mirror and the distances towards the left side of the mirror are always negative.

★Image distances (v) for a convex mirror is always positive because the image is always formed behind the mirror.But in case of concave mirror it can be either positive or negative.This is because distances measured to the left of the mirror are negative and to the right of the mirror is positive.