Which of the following is the correct general form of Snell's law?

What changes; frequency or wavelength, when light passes from a rarer to a denser medium?

Which of the following is a part of a spherical mirror?

$(a)$ Write one use of a concave mirror as well as a convex mirror.
$(b)$ Draw ray diagrams for the following cases when a ray of light:
$(i)$ passing through the centre of curvature of a concave mirror is incident on it.
$(ii)$ parallel to the principal axis is incident on a convex mirror.
$(iii)$ is incident at the pole of a convex mirror.
$(iv)$ passing through the focus of a concave mirror is incident on it.

If the image formed by a mirror for all positions of the object placed in front of it is always erect and diminished,what type of mirror is it? Draw a ray diagram to justify your answer. Where and why do we generally use this type of mirror?

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.