The relation between $n_1$ and $n_2$,if the behavior of light rays is as shown in the figure,is:

Consider a plane parallel beam of light incident on a plano-cylindrical lens as shown below. Which of the following will you observe on a screen placed at the focal plane of the lens?

$A$ lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I.$ If an aperture of diameter $\frac{d}{2}$ in the central region of the lens is covered by a black paper,the focal length of the lens and the intensity of the image will be,respectively:

An object is placed at the focus of a concave lens having focal length $f$. What is the magnification and distance of the image from the optical centre of the lens?

$A$ convex lens is placed between an object and a screen which are at a fixed distance $D$ apart. For one position of the lens,the magnification of the image formed on the screen is $m_1$. When the lens is shifted by a distance $d$,the magnification of the image formed on the same screen is $m_2$. The focal length of the lens is:

An equiconvex lens of radius of curvature $14 \ cm$ is made up of two different materials. The left half and right half of the vertical portion are made up of materials with refractive indices $1.5$ and $1.2$ respectively,as shown in the figure. If a point object is placed at a distance of $40 \ cm$,calculate the image distance. (in $cm$)