An object is placed at a distance of $12 \ cm$ in front of a concave mirror. It forms a real image four times larger than the object. Calculate the distance of the image from the mirror. (in $cm$)

For what position of the object does a concave mirror form a real and diminished image?

The refractive indices of turpentine oil,kerosene,and alcohol are $1.47, 1.44$,and $1.36$ respectively. Based on this information,complete the following ray diagrams to show the path of a ray of light through each medium. (Give a reason for your answer.)

The velocity of light in a vacuum is $....$

$A$ $5 \, cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $20 \, cm$. The distance of the object from the lens is $30 \, cm$. Find the $(i)$ position,$(ii)$ nature,and $(iii)$ size of the image formed.

Write the relationship between object distance $(u)$,image distance $(v)$,and focal length $(f)$ for a spherical mirror.