If a concave lens is placed in the path of converging rays,a real image will be produced if the distance of the pole from the point of convergence of incident rays lies between ($f =$ magnitude of focal length of lens).

$A$ biconvex lens of radius of curvature $R$ is made up of a variable refractive index $\mu = 2[1 + \frac{|y|}{d}]$. Assume $2d << R$. $A$ point object is placed at a distance $R$ on the principal axis as shown in the figure. If the spread of the image lies over a span of $n$ meters,find the value of $n$.

The refractive index of a material of a plano-concave lens is $5/3$, and the radius of curvature is $0.3 \,m$. The focal length of the lens in air is (in $\,m$)

The sun subtends an angle of $0.5^{\circ}$ at the earth's surface. Its image is formed by a convex lens of focal length $50 \ \text{cm}$. The diameter of the image will be (in $\text{mm}$)

An object of size $3.0 \, cm$ is placed $14 \, cm$ in front of a concave lens of focal length $21 \, cm$. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

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?