How will you decide whether a given piece of glass is a convex lens,concave lens,or a plane glass plate?

Which of the following ray diagrams is correct for the ray of light incident on a lens shown in the figure?

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.

$(a)$ Define the optical centre of a spherical lens.
$(b)$ You are given a convex lens of focal length $30 \, cm$. Where would you place an object to get a real,inverted,and highly enlarged image of the object? Draw a ray diagram showing the image formation.
$(c)$ $A$ concave lens has a focal length of $20 \, cm$. At what distance from the lens should an object be placed so that it forms an image at $15 \, cm$ away from the lens?

$(a)$ Why does a ray of light passing through the centre of curvature of a concave mirror after reflection get reflected back along the same path?
$(b)$ Why are convex mirrors commonly used as rear-view mirrors in vehicles?
$(c)$ $A$ pencil partly immersed in water in a glass tumbler appears to be displaced at the interface of air and water. Name the phenomenon of light responsible for it.

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