A convex lens of focal length ' $f$ ' produces a real image whose size is ' $n$ ' times the size of an…

A convex lens of focal length ' $f$ ' produces a real image whose size is ' $n$ ' times the size of an object. The distance of the object from the lens is
  1. $\frac{\mathrm{n}+1}{\mathrm{nf}}$
  2. $\mathrm{f}\left(1-\frac{1}{\mathrm{n}}\right)$
  3. $\frac{\mathrm{nf}}{\mathrm{n}+1}$
  4. $\mathrm{f}\left(1+\frac{1}{\mathrm{n}}\right)$

Solution

Given, $\therefore \quad$ Image distance, $v=-n u$ $\begin{aligned} \quad \frac{1}{\mathrm{f}} & =\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{-\mathrm{nu}}-\frac{1}{\mathrm{u}}=\frac{\mathrm{u}+\mathrm{nu}}{n u^2} \\ \therefore \quad \frac{1}{\mathrm{f}} & =\frac{1+\mathrm{n}}{\mathrm{nu}} \\ \mathrm{u} & =\mathrm{f}\left(\frac{1+\mathrm{n}}{\mathrm{n}}\right)=\mathrm{f}\left(1+\frac{1}{\mathrm{n}}\right) \end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 2)

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