An object is placed at a distance of $40\, cm$ in front of a concave mirror of focal length $20\, cm$. The image produced is

Give the relationship of magnification with focal length of a spherical mirror.

An object is situated at $8 \, cm$ from a convex lens of focal length $10 \, cm$. Find the position and nature of the image. Draw a ray diagram to illustrate the formation of the image (not to scale).

Draw ray diagrams showing the image formation by a concave mirror when an object is placed:
$(a)$ Between pole $(P)$ and focus $(F)$ of the mirror.
$(b)$ Between focus $(F)$ and centre of curvature $(C)$ of the mirror.
$(c)$ At centre of curvature $(C)$ of the mirror.
$(d)$ $A$ little beyond centre of curvature $(C)$ of the mirror.
$(e)$ At infinity.

The diagram given below shows an object $O$ and its image $I.$ Copy the diagram and draw suitable rays to locate the lens and its focus. Name the type of lens in this case.

$(a)$ 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?