Which of the following can produce a magnification of $+0.5$?

$A$ point object emits rays in all directions. Consider a ray emitted from the object that is parallel to the principal axis of the mirror. One of the points required to trace the reflected ray is the point of incidence itself,as shown in the figure. Select a point from the given figure through which the reflected ray passes.

Name the type of lens that can be used as a magnifying glass. Give reason$(s)$ and draw a ray diagram to support your answer.

The refractive indices of medium $(1)$ and medium $(2)$ are $\eta_{1}$ and $\eta_{2}$ respectively,and the velocities of light in these media are $v_{1}$ and $v_{2}$ respectively. What is the formula to find the refractive index of medium $(2)$ with respect to medium $(1)$,denoted as $\eta_{21}$?

What can be measured using a dioptre meter?

$A$ 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.