Question

Show that a convex lens produces an N times magnified image when the object distances, from the lens have magnitudes (f+f/N) or (f-f/N). f is magnitude of focal length of lens​

Answer 1

Explanation:

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Answer 2

The magnitude of the object distance is $f\pm\dfrac{f}{N}$

Explanation:

Given that,

Focal length = f

Magnification = ±N

We need to calculate the magnitude of the object distance

Using formula of magnification

$m = \dfrac{v}{u}....(I)$

Where, v = image distance

u = object distance

Using lens formula

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

$\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}$

$v=\dfrac{uf}{u+f}$

Put the value of v  in equation (I)

$m=\dfrac{\dfrac{uf}{u+f}}{u}$

$m=\dfrac{f}{u+f}$

Put the value of magnification

$\pm N=\dfrac{f}{u+f}$

$u+f=\pm \dfrac{f}{N}$

$u=-f\pm\dfrac{f}{N}$

$|u|=f\pm\dfrac{f}{N}$

Hence, The magnitude of the object distance is $f\pm\dfrac{f}{N}$

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Topic : optics

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