An object is placed at a distance of $5 \, cm$ from the first principal focus of a convex lens of focal length $10 \, cm$. If a real image is formed,find its distance from the lens in $cm$.

At what distance from a biconvex lens of focal length $F$ must an object be placed so that the distance between the object and its real image is minimal?

$A$ student measures the focal length of a convex lens by placing an object pin at a distance '$u$' from the lens and measuring the distance '$v$' of the image pin. The graph between '$u$' and '$v$' plotted by the student should look like:

$A$ plano-convex lens is made of glass with a refractive index of $1.5$. The radius of curvature of its convex surface is $R$. What is its focal length?

Assertion: Goggles have zero power.
Reason: Radius of curvature of both sides of the lens is same.

Consider the following statements regarding the real images formed with a converging lens.
$I$. Real images can be seen only if the image is projected onto the screen.
$II$. The real image can be seen only from the same side of the lens as that on which the object is positioned.
$III$. Real images produced by converging lenses are not only laterally but also longitudinally inverted as with mirrors.
Which of the above statement$(s)$ is/are incorrect?