What is the nature of the image formed by an object placed at a distance of $10 \text{ cm}$ in front of a concave mirror with a focal length of $20 \text{ cm}$?

An object $4 \ cm$ high is placed at a distance of $27 \ cm$ in front of a convex lens of focal length $18 \ cm$. Find the position,nature,and size of the image formed.

If the angle of incidence on a plane mirror is $30^{\circ}$,what is the angle of reflection (in $^{\circ}$)?

$(a)$ 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.

One half of a convex lens of focal length $10\, cm$ is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of $30\, cm$ from the lens? Draw a ray diagram to justify your answer.
$A$ $4\, cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $20\, cm$. The distance of the object from the lens is $15\, cm$. Find the nature,position and size of the image.

$(a)$ Define radius of curvature and focal length of a spherical mirror and show it on a figure.
$(b)$ Write the relation between the radius of curvature and the focal length of a spherical mirror.