Question

A 1 cm high object is placed at a distance of 2F from a convex lens, what is the height of the
image formed?​

Answer 1

$\huge\sf\pink{Answer}$

☞ The height of the image is 1 cm

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$\huge\sf\blue{Given}$

✭ Image distance is 2f

✭ Lens = Convex lens

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$\huge\sf\gray{To \:Find}$

◈ Height of the image formed?

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$\huge\sf\purple{Steps}$

So the lens formula is given by,

$\underline{\boxed{\sf \dfrac{1}{v}-\dfrac{1}{u} = \dfrac{1}{f}}}$

• F = Focal Length
• u = Object Distance
• v = Image distance

Substituting the given values,

➝ $\sf \dfrac{1}{v}-\dfrac{1}{u} = \dfrac{1}{f}$

➝ $\sf \dfrac{1}{2f}-\dfrac{1}{u} = \dfrac{1}{f}$

➝ $\sf \dfrac{1}{v} = \dfrac{1}{f}-\dfrac{1}{2f}$

➝ $\sf \dfrac{1}{v} = \dfrac{2-1}{2f}$

➝ $\sf \dfrac{1}{v} = \dfrac{1}{2f}$

➝ $\sf \green{v=2f}$

Magnification is given by,

➳ $\sf M = \dfrac{v}{u}$

➳ $\sf M = \dfrac{2f}{2f}$

➳ $\sf \red{M = 1}$

We also know that,

$\underline{\boxed{\sf M = \dfrac{h'}{h}}}$

• M = Magnification
• h' = Height of image
• h = Height of object

Substituting the given values,

»» $\sf M = \dfrac{h'}{h}$

»» $\sf 1 = \dfrac{h'}{1}$

»» $\sf 1\times 1 = h'$

»» $\sf \orange{h' = 1}$

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