Question

The size of image of an object by a convex lens of Focal Length 20 cm is observed to be reduced to 1/3 rd of its size . Find the distance of the object from the optic center of the lens ?

please answer the above Question

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Answer 1

40cm is the answer am I right

Answer 2

Answer:

The distance of the object from the optic center of the lens = 80 cm

Step-by-step explanation:

Given Focal length $(f)=20\text{ cm}$

Consider the height of the object =$h_{o}=x\text{ cm}$

As per the question the height of the image is 1/3 rd of object height = $h_{i}=\frac{1}{3}x\text{ cm}$

consider the distance of the object from the optic center of the lens is =$d_{o}$

the distance of the image from the optic center of the lens is =$d_{i}$

we know that

$\frac{h_{i}}{h_{o}}=\frac{d_{i}}{d_{o}}\\\\\frac{\frac{1}{3} x}{x}=\frac{d_{i}}{d_{o}}\\\\\frac{1}{3}=\frac{d_{i}}{d_{o}}\\\\{d_{i}}=\frac{d_{o}}{3}$

Form the thin lens equations we find that

$\frac{1}{d_{o}}+\frac{1}{d_{i}}=\frac{1}{f}\\\\\Rightarrow\frac{1}{d_{o}}+\frac{1}{\frac{d_{o}}{3}}=\frac{1}{f}\\\\\Rightarrow\frac{1}{d_{o}}+\frac{3}{d_{o}}=\frac{1}{20}\\\\\Rightarrow\frac{4}{d_{o}}=\frac{1}{20}\\\\\Rightarrow{d_{o}=80$

Therefore, the distance of the object from the optic center of the lens = 80 cm