$A$ boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length $10\, cm$. The diameter of the sun is $1.39 \times 10^9\, m$ and its mean distance from the earth is $1.5 \times 10^{11}\, m$. What is the diameter of the sun's image on the paper?

For a convex lens,if a real image is formed,the graph between $(u + v)$ and $u$ or $v$ is as follows:

Calculate the focal length of the given lens in $cm$,if the magnification is $-0.5$.

$A$ screen is placed $90 \; cm$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20 \; cm$. Determine the focal length (in $cm$) of the lens.

If the focal lengths of red and violet light rays for the same lens are $f_R$ and $f_v$ respectively,then which of the following is true?

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?