Question

Figure. shows variation of magnification $m$ (produced by a thin convex lens) and distance $v$ of image from 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 of the above

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

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$1-\frac{v}{u}=\frac{v}{f}$
Since $m$ is positive in the given figure, therefore $m$ represents magnitude of the magnification. In fact, if a real image is formed by a convex len, then the image and object will be on opposite sides of the lens. It means, if $v$ is positive, then $u$ will be negative. Therefore,
$m=\left|\frac{v}{u}\right|=-\frac{v}{u}$
Hence, Eq. (i) becomes
$m=\frac{v}{f}-1....\left(ii\right)$
It means, the graph between $m$ and $v$ will be a straight line having intercept $-1$ and $m-axis$ and slope of the line $\tan \theta$ is equal to $\left(1/f\right)$. Hence, option (b) and (c) are correct. Putting $m=0$ in Eq. (ii), $v=f$. Hence, (a) is also correct. Obviously, (d) is wrong.