$A$ thin lens has a focal length of $-12\, cm$. Is it a convex lens or a concave lens?

$(a)$ State the laws of refraction.
$(b)$ $A$ ray of light enters from a medium $A$ into a slab made up of a transparent substance $B$ (as shown in the figure). The refractive indices of medium $A$ and $B$ are $2.42$ and $1.65$ respectively. Complete the path of the ray of light until it emerges out of the slab.

An object $3.0 \text{ cm}$ high is placed perpendicular to the principal axis of a concave lens of focal length $7.5 \text{ cm}$. The image is formed at a distance of $5.0 \text{ cm}$ from the lens. Calculate $(i)$ distance at which object is placed,and $(ii)$ size and nature of image formed.

Write two important applications of $(i)$ concave mirror and $(ii)$ convex mirror.

The mirror formula describes the relationship between the height of the image and the height of the object.

Which of the following can produce a magnification of $+5$ as well as $-5$?