An object $1 \, cm$ tall is placed at a distance of $15 \, cm$ from a concave mirror of focal length $10 \, cm$. Find the position,size,and nature of the image formed.

One half of a convex lens is covered with a black paper.
$(a)$ Show the formation of the image of an object placed at $2F_{1}$ of such a covered lens with the help of a ray diagram. Mention the position and nature of the image.
$(b)$ Draw the ray diagram for the same object at the same position in front of the same lens,but now uncovered. Will there be any difference in the image obtained in the two cases? Give a reason for your answer.

How many centres of curvature does a lens have?

$A$ 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.

Two adjacent walls and the ceiling of a rectangular room are mirror surfaced. The number of images of himself that an observer sees is

In a plane mirror,the distance between the image and the mirror is the same as the distance between the object and the mirror.