What is the focal length of a plane mirror?

$(i)$ Under what condition does a concave mirror produce a virtual and magnified image? Draw a labelled ray diagram to show the formation of the image in the above case. Also,state the position of the object to produce a magnified and real image.
$(ii)$ $A$ ray of light moving along the principal axis is falling on a concave mirror. Draw the path of the reflected ray. Also,state the values of the angle of incidence and reflection in this case.

What is the absolute refractive index of common glass?

$(i)$ Define a real image of an object.
$(ii)$ Name the mirror that:
$(a)$ can give a real as well as a virtual image of an object.
$(b)$ will always give a virtual image of the same size as the object.
$(c)$ will always give a virtual and diminished image of an object.
$(d)$ is used by a doctor in examining teeth.
$(iii)$ With the help of a ray diagram,explain the use of a concave mirror as a solar concentrator.

$A$ ray of light $AB$ parallel to the principal axis is incident on a convex lens as shown in the figure. Copy the figure.
$(i)$ Draw the refracted ray.
$(ii)$ Name the point through which the refracted ray passes on the principal axis.

For the same angle of incidence in media $P, Q$ and $R$,the angles of refraction are $45^{\circ}, 35^{\circ}$ and $15^{\circ}$ respectively. In which medium will the velocity of light be minimum? Give reason.