To understand why the correct answer is option 'C' (between F1 and 2F1), let's first review the basic properties of convex lenses and the formation of images.

Properties of Convex Lenses:
1. Convex lenses are thicker at the center and thinner at the edges.
2. They converge parallel rays of light that pass through them.
3. They have two focal points, F1 and F2, located on either side of the lens.

Formation of Images:
When an object is placed in front of a convex lens, the lens refracts the light rays coming from the object. The refracted rays converge to form an image on the other side of the lens.

Now, let's analyze the different options:

a) At 2F1:
If the object is placed at 2F1, the refracted rays will converge and meet at F2. As a result, the image will be formed at F2. This means that the image will be located on the same side as the object, which is not the desired outcome for a slide projector. Therefore, option 'a' is incorrect.

b) At F1:
If the object is placed at F1, the refracted rays will become parallel after passing through the lens. Parallel rays do not converge, so no image will be formed. This means that the image will be at infinity, which is not practical for a slide projector. Therefore, option 'b' is incorrect.

c) Between F1 and 2F1:
When the object is placed between F1 and 2F1, the refracted rays will converge and meet beyond 2F1, forming a real and inverted image. This image can be projected onto a screen or slide. Placing the object at this position allows for a clear and focused image to be formed on the slide projector. Therefore, option 'c' is the correct answer.

d) Beyond F1:
If the object is placed beyond F1, the refracted rays will still converge, but the image will be formed on the same side as the object, which is not desired for a slide projector. Therefore, option 'd' is incorrect.

In summary, placing the object between F1 and 2F1 allows for a real and inverted image to be formed on a slide projector. This position ensures a clear and focused image projection.