For what position of the object does a concave mirror form a real and diminished image?

$A$ 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.

$A$ $2.0 \text{ cm}$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $10 \text{ cm}$. The distance of the object from the lens is $15 \text{ cm}$. Find the position,nature,and size of the image formed.

The focal length of a plane mirror is $.....$

$A$ concave mirror can be used to obtain a parallel beam of light from a small lamp.

$(a)$ Two lenses have powers of $(i) +2 \text{ D}$ and $(ii) -4 \text{ D}$. What is the nature and focal length of each lens?
$(b)$ An object is kept at a distance of $100 \text{ cm}$ from a lens of power $-4 \text{ D}$. Calculate the image distance.