Question

To form an enlarged image of an object in front of a convex lens, it should be placed _____.
$1$. anywhere between $2F$ and O
$2$. behind the focal point
$3$. at the centre of curvature
$4$. at $2F$

Answer 1

When an object is located between the centre of curvature and focus, the actual image is made behind the centre of curvature. The size of the image is more significant than the object. When an object is set at the focus, an actual image is made at infinity. The image size is much bigger than the object. When an object is set in between focus and pole, a virtual image is created. The size of the image is more significant than that of the object.

Complete answer:
When an object is put between the focus and centre of curvature, then a ray parallel to the principal axis after refraction moves through focus F. While the other ray passes through the optical centre C and goes through without any divergence. These two refracted light rays cross, and the image formed is larger than the object, real and inverted.

When an object is set at the principal focus F, a ray parallels the principal axis after refraction travel through the focus; simultaneously, the other ray passes through the optical centre and goes uninterrupted. Both the refracted rays are parallel to each other and cannot cross each other. Hence the image will be created at infinity. The image formed is highly enlarged, real, and inverted.

When an object is set between the principal focus and optical centre of a convex lens, a parallel ray crosses through the focus after refraction. The other ray moves through the optical centre and goes uninterrupted. Two refracted rays cannot meet to form an original image. Thus, the refracted rays are continued backward by dotted lines—a virtual, erect, and highly enlarged image made on the same side of the lens.

To form an enlarged image of an object in front of a convex lens, it should be placed anywhere between $2F$ and O.

Option ($1$) is correct.

Note:
When an object is located at some distance from the lens then between the pole and the focus, a virtual image is formed of the convex lens. The image size is much less than the size of the object. There are some rules for the ray to travel: When a ray falls on convex lenses diagonally at its pole, it follows its path. When a ray is parallel to the principal axis, the reflected ray moves through a focus. When a ray, moving through focus, the ray will then move parallel to the principal axis.