Draw the ray diagram in each case to show the position,nature,and size of the image formed when the object is placed:
$(i)$ At the centre of curvature of a concave mirror.
$(ii)$ Within the focal length of a convex lens.
$(iii)$ Between the pole and focus of a concave mirror.
$(iv)$ In front of a convex mirror.
$(v)$ In front of a concave lens.

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(N/A) $(i)$ At the centre of curvature $(C)$ of a concave mirror: The image is formed at $C$,is real,inverted,and of the same size as the object.
$(ii)$ Within the focal length $(f)$ of a convex lens: The image is formed on the same side as the object,is virtual,erect,and magnified.
$(iii)$ Between the pole $(P)$ and focus $(F)$ of a concave mirror: The image is formed behind the mirror,is virtual,erect,and magnified.
$(iv)$ In front of a convex mirror: The image is formed behind the mirror between the pole and focus,is virtual,erect,and diminished.
$(v)$ In front of a concave lens: The image is formed between the optical centre and focus on the same side as the object,is virtual,erect,and diminished.

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An object is placed at the following distances from a concave mirror of focal length $15 \, cm$.
$(a)$ $10 \, cm$ $(b)$ $20 \, cm$ $(c)$ $30 \, cm$ $(d)$ $40 \, cm$
Which position of the object will produce:
$(1)$ Virtual image
$(2)$ $A$ diminished real image
$(3)$ An enlarged real image
$(4)$ An image of same size

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