What is meant by the radius of curvature of a spherical mirror? How is it related to the focal length of the mirror?

What is a lens?

$(a)$ $A$ thin converging lens forms a:
$(i)$ Real magnified image.
$(ii)$ Virtual magnified image of an object placed in front of it.
Write the positions of the objects in each case.
$(b)$ Draw labelled ray diagrams to show the image formation in each case.
$(c)$ How will the following be affected on cutting this lens into two halves along the principal axis?
$(i)$ Focal length,
$(ii)$ Intensity of the image formed by half lens.

$(i)$ Describe an activity to find the approximate value of the focal length of a concave mirror.
$(ii)$ What happens to the size of the image of an object when it is moved gradually away from a convex mirror?
$(iii)$ In an experiment to study refraction through a glass slab,it is observed that a ray of light undergoing refraction emerges parallel to the direction of the incident ray. Why does it happen so? Explain with the help of a diagram.

$(a)$ Calculate the distance at which an object should be placed in front of a convex lens of focal length $10\, cm$ to obtain a virtual image of double its size.
$(b)$ In the above given case,find the magnification,if the image formed is real. Express it in terms of the relation between $v$ and $u$.

An object is placed at a distance of $20 \text{ cm}$ in front of a concave mirror of focal length $10 \text{ cm}$. Where will the image be formed?