Q146 / 160 · AP EAMCET 2021 (24 Aug Shift 2) · Physics

The focal length of a convex lens is $f$. An object is placed at a distance $x$ from its first focal point. The ratio of the size of the real image to that of the object is

  • A
    $\frac{f}{x^2}$
  • B
    $\frac{x^2}{f}$
  • Correct answer
    C
    $\frac{f}{x}$
  • D
    $\frac{x}{f}$

Solution

Given that, focal length of convex lens $=f$ Distance of object from lst focus point $=x$ Now, object distance, $u=-(f+x)$ We know that, ratio of size of real image to that of object = magnification which is given by $m=\frac{v}{u}=\frac{f}{f+u}$ $\Rightarrow \quad m=\frac{f}{f-(f+x)}=-\frac{f}{x}$ Taking magnitude only, $|m|=\frac{f}{x}$.

Hence, the correct answer is option: 'C'.

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