State whether true or false:
A convex lens has a divergent action and a concave lens has a convergent action.
A. True
B. False

Hint: Check what happens to the rays of lights when they pass through (i) a convex lens (ii) a concave lens. With this, you will get to know which one has a divergent action and one has a convergent action.

Complete step by step answer:
Lens is a transparent medium bounded by two refracting surfaces, such that at least one surface is spherical. There are mainly two types of lenses- convex lens and concave lens. Convex lens is also called converging lens and concave is also called diverging lens. Convex lens is thick at the middle and the thickness decreases until the end. Concave lens is thinnest at the middle and the thickness increases until the end.
When light from an object passes through these lenses they refract the light and form an image of that object. This is given by the formula $\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$ , where u is the position of the object from the lens and v is the position of the image formed from the lens (according to sign convection) . f is the distance of the focus from the lens.
For a convex lens, the value of f is taken positive and for a concave lens, the value f is taken negative.
When parallel rays of light pass through a convex lens, all of them converge at a single point i.e. the focus of the lens. Hence, a convex lens is also called a converging lens.

When the same parallel rays of light pass through a concave lens, all the rays diverge in all directions such that they seem to be coming from the focus of the lens. Hence, a concave lens is also called a diverging lens.

The given statement in the question says that a convex lens has a divergent action and a concave lens has convergent action. However, what we learnt now says just the opposite of this statement. Therefore, the given statement is false.
Hence, the correct option is B.

Note: Do not confuse between the convergence or divergence of a curved mirror and a lens of the same names.
A concave mirror is a converging mirror whereas a concave lens is a diverging lens.
A convex mirror is a diverging mirror whereas a convex lens is a converging lens.