$A$ 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:

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-convex lens and second image from the convex 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?

When will the convergent nature of a convex lens be less as compared to its nature in air?

The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 \,cm$. If the radii of curvature are equal, the value of the radius of curvature (in $cm$) is

$A$ 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:

$A$ lens of focal length $f$ and diameter $d$ forms an image of intensity $I$. If the central part of the lens of diameter $\frac{d}{2}$ is covered with a paper,what will be the new focal length and the new intensity of the image?