How will you distinguish between a convex and a concave lens without touching them?

$A$ convex lens has a focal length of $25\, cm$. Calculate the distance of the object from the lens if the image is to be formed on the opposite side of the lens at a distance of $75\, cm$ from the lens. What will be the nature of the image?

Find the focal length of a convex lens,if its power is $+2.0 \ D$. (in $m$)

The nature,size,and position of the image of an object produced by a lens or mirror are as shown below. Identify the lens/mirror $(X)$ used in each case and draw the corresponding complete ray diagram.

$(a)$ Write the relation between $u, v, f$ for lenses and for mirrors,where $u, v, f$ are object distance,image distance,and focal length respectively.
$(b)$ The magnification produced by a concave mirror is $m = +4$. Write the information about the image given by this statement.
$(c)$ Draw a ray diagram for the following and show the formation of the images in the case of a concave mirror when the object is placed:
$(i)$ Between the pole and the focus point.
$(ii)$ At the centre of curvature.

Under which of the following conditions can a concave mirror form an image larger than the actual object?