Photographs of the ground are taken from an aircraft flying at an altitude of $2000\; m$ by a camera with a lens of focal length $50\; cm$. The size of the film in the camera is $18\; cm \times 18\; cm$. The area of the ground that can be photographed by the camera is

Consider an equi-convex lens of glass $\left( \mu = \frac{3}{2} \right)$. If the temperature of the lens is increased by $40\, ^\circ C$,its focal length remains the same. The coefficient of linear expansion of glass is $2.5 \times 10^{-4} / ^\circ C$. Calculate the change in the refractive index of the glass on increasing the temperature by $40\, ^\circ C$.

The magnification of an object placed in front of a convex lens of focal length $20 \, cm$ is $+2$. To obtain a magnification of $-2$,the object has to be moved a distance equal to.....$cm$

The word $KVPY$ is written on a board and viewed through different lenses such that the board is at a distance beyond the focal length of the lens.
Ignoring magnification effects,consider the following statements.
$(I)$ First image has been viewed from the planar side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$(II)$ First image has been viewed from the concave side of a plano-concave lens and second image from the convex side of a plano-convex lens.
$(III)$ First image has been viewed from the concave side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$(IV)$ First image has been viewed from the planar side of a plano-concave lens and second image from the convex side of a plano-convex lens.
Which of the above statements are correct?

$A$ 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:

When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material of the lens,the focal length of the lens increases by $100 \%$. The refractive index of the liquid is