Question

Figure shows variation of magnification m (produced by a thin convex lens) and distance $v$ of image from the pole of the lens. Which of the following statements are correct?

• A. Focal length of the lens is equal to intercept on $v$-axis.
• B. Focal length of the lens is equal to inverse of slope of the line.
• C. Magnitude of intercept on $m$-axis is equal to unity.
• D. None

Answer 1

Answer: (A), (B), (C)

The correct options are
A Focal length of the lens is equal to intercept on $v$-axis.
B Focal length of the lens is equal to inverse of slope of the line.
C Magnitude of intercept on $m$-axis is equal to unity.

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow 1-\frac{v}{u}=\frac{v}{f}$
$\Rightarrow m=\frac{-v}{u}=\frac{u-f}{f}=\frac{v}{f}-1$ ---(1)
Comparing (1) with $y=kx+c$ where $k$ is the slope & $c$ is the intercept on $m$-axis, we get slope $=\tan \theta =\frac{1}{f}$
and $c=-1$ (B & C)

Intercept on $v$-axis is given by
$m=0\Rightarrow v=f$ (A)