A hollow lens is made of thin glass and in the shape of a double concave lens. It can be filled with air, the water of refractive index $1.33$ or ${\mathrm{CS}}_2$ of refractive index $1.6$. It will act as a diverging lens if it is

The word "KVPY" is written on board and viewed through different lenses such that board is at a distance beyond the focal length of the lens.

Ignoring magnification effects, consider the following statements.
(I) Image $\left(i\right)$ has been viewed from the planar side of a plano-convex lens and image
(ii) from the convex side of a plano-convex lens.
(II) Image $\left(i\right)$ has been viewed from the concave side of a plano-concave lens and image $\left(ii\right)$ from the convex side of a plano-convex lens.
(III) Image $\left(i\right)$ has been viewed from the concave side of a plano-concave lens and image $\left(ii\right)$ from the planar side of a plano-convex lens.
(IV) Image $\left(i\right)$ has been viewed from the planar side of a plano-concave lens and image $\left(ii\right)$ from the convex side of a plano-convex lens.

Which of the above statements are correct?

A student studying the similarities and differences between a camera and the human eye makes the following observations:
(I) Both the eye and the camera have convex lenses.
(iI) In order to focus, the eye lens expands or contracts while the camera lens moves forward or backward.
(III) The camera lens produces upside-down real images while the eye lens produces only upright real images.
(IV) A screen in a camera is equivalent to the retina in the eyes.
(V) A camera adjusts the amount of light entering it by adjusting the aperture of the lens. In the eye, the cornea controls the amount of light.

The correct statements are :

A long horizontal mirror is next to a vertical screen (see figure). Parallel light rays are falling on the mirror at an angle $\alpha$ from the vertical. If a vertical object of height $h$ is kept on the mirror at a distance $d>h\tan \left(\alpha \right)$. The length of the shadow of the object on the screen would be-