$A$ $10\, mm$ long awl pin is placed vertically in front of a concave mirror. $A$ $5\, mm$ long image of the awl pin is formed at $30\, cm$ in front of the mirror. The focal length of this mirror is ......... $cm$.

An object of height $5 \, cm$ is placed perpendicular to the principal axis of a concave lens of focal length $10 \, cm$. If the distance of the object from the optical centre of the lens is $20 \, cm$,determine the position,nature,and size of the image formed using the lens formula.

Both a spherical mirror and a thin spherical lens have a focal length of $-15 \; cm$. What type of mirror and lens are they?

Which of the following has the minimum refractive index?

$A$ $2.0 \text{ cm}$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $10 \text{ cm}$. The distance of the object from the lens is $15 \text{ cm}$. Find the position,nature,and size of the image formed.

The absolute refractive indices of water,glass,and diamond are $1.33$,$1.50$,and $2.42$ respectively. Which medium is the most optically dense?