Read the following statements and choose the correct option. (A) Only a point source forms a complete umbra. (B) An extended source of light forms both umbra and penumbra. (1) Only A is true (2) Only B is true (3) Both A and B are true (4) Both A and B are false

A point source of light is an idealization - it is a source of light that emits light rays in all directions, originating from a single point. In reality, this doesn't exist, but it's a useful approximation for sources that are much smaller than the distances involved in the problem. An extended source of light, on the other hand, has a finite size and emits light from its entire surface area, such as the sun.

Umbra is the region of complete shadow where no light from the source reaches. Penumbra is a partially lit area where some light from the source reaches, but not all of it. In the case of a point source, all light rays from the single point diverge and can be blocked entirely by an object, creating a complete umbra. In contrast, for an extended source of light, since light is emanating from various points on its surface, an object can block light rays from some parts of the source but not others, leading to the formation of both umbra (where light from the entire source is blocked) and penumbra (where light from part of the source is blocked). Now that we understand these concepts, we can evaluate the given statements.

Statement A says that only a point source forms a complete umbra. As described earlier, this statement is true since a point source emits light from a single point, and when an object blocks this light, it creates a region of complete shadow, i.e., umbra.

Statement B states that an extended source of light forms both umbra and penumbra. This statement is also true, as explained previously that due to the finite size of the extended source and light coming from various parts of its surface, blocking of the light by an object can create regions of both complete shadow (umbra) and partial shadow (penumbra).

Since both statements A and B are true, the correct option is (3) Both A and B are true. Hence, the answer is (3).