Question

A convex lens of focal length f produces an image 1/n times that of the size of the object. The distance of the object from the lens is........................(please explain it)

Answer 1

$m=\frac{v}{u}=-\frac{1}{n}\\\\u=-vn\\\\ The\ lens\ formula\ is: \\\\\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\\\\frac{1}{v}-\frac{1}{-vn}=\frac{1}{f}\\\\ v=\frac{(n+1)}{n}f\\\\ u = object\ distance\ from\ lens=u=-vn=-(n+1)f$

Answer 2

Answer:

$f( n- 1)$

Explanation:

according to the question,

$\frac{v}{u} = \frac{1}{n} \\ \\ u = vn$

. --------1

Therefore using lens formula,

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ \\ \frac{1}{f} = \frac{n - 1}{n} \\ \\ v = \frac{f(n - 1)}{n}$

using (1) equation...—

$u = f(n - 1)$

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