Explain why drivers prefer to use a convex mirror as a rearview mirror in automobiles.

$A$ beam of light is incident through the holes on side $A$ and emerges out of the holes on the other face of the box as shown in the Figure. Which of the following could be inside the box?

Light enters from air into diamond,which has a refractive index of $2.42$. Calculate the speed of light in diamond. The speed of light in air is $3.0 \times 10^{8} \text{ m s}^{-1}$.

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

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

$A$ 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.