Question

Assertion :The minimum distance between an object and its real image formed by a convex lens is ${}^{\prime }2f{}^{\prime }$ Reason: The distance between object and its real image is minimum when its magnification is one.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is incorrect but Reason is correct.
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is incorrect but Reason is correct.

Let the between object and real image be $d$.

Let the distance of object from the lens is $x$ i.e. $u=-x$

So the distance of image and lens be $d-x$

Using the lens equation

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{f}=\frac{1}{d-x}-\frac{1}{-x}$

$x=\frac{d\pm \sqrt{d^2-4fd}}{2}$ ...(1)

So for real x

$\sqrt{d^2-4fd}\ge 0$

So $d\ge 4f$

So minimum distance between object and image is 4f.

Putting $d=4f$ in equation 1

We get $x=\frac{d}{2}$

Distance of image from lens is $d-x=d/2$

$m=\frac{v}{u}=\frac{d/2}{d/2}=1$

Reason is correct but assertion is not true.