State the sign convention used to measure the length of the image and the object.

What is the unit of refractive index?

What is the speed of light waves in a vacuum in units of $km/s$?

$A$ student focused the image of a candle flame on a white screen by placing the flame at various distances from a convex lens. He noted his observations:

Observation	Distance of flame from the lens $(cm)$	Distance of screen from the lens $(cm)$
$(i)$	$60$	$20$
$(ii)$	$40$	$24$
$(iii)$	$30$	$30$
$(iv)$	$24$	$40$
$(v)$	$15$	$70$

$(a)$ From the above table, find the focal length of the lens without using the lens formula.
$(b)$ Which set of observations is incorrect and why?
$(c)$ In which case will the size of the object and the image be the same? Give a reason for your answer.

State the sign convention for lenses regarding object and image distances.

$(a)$ $A$ concave mirror produces a three times enlarged real image of an object placed at $10\, cm$ in front of it. Calculate the focal length of the mirror.
$(b)$ Show the formation of the image with the help of a ray diagram when an object is placed $6\, cm$ away from the pole of a convex mirror.