In torches,searchlights,and headlights of vehicles,the bulb is placed:

Draw ray diagrams showing the image formation by a convex lens when an object is placed:
$(a)$ Between optical centre and focus of the lens.
$(b)$ Between focus and twice the focal length of the lens.
$(c)$ At twice the focal length of the lens.
$(d)$ At infinity.
$(e)$ At the focus of the lens.

$A$ 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.

When an object is placed between the principal focus $(F)$ and the pole $(P)$ of a concave mirror,what kind of image is formed?

$(i)$ 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.

What is the type of the final image,as compared to the object,in the compound microscope?