When an object is placed 15 cm from a lens, a virtual image is formed. Mark the correct statements.

A.)The lens may be convex or concave
B.)If the lens is diverging, the image distance has to be less than 15 cm
C.)If the lens is converging, then its focal length has to be greater than 15 cm
D.)All of the above

Hint:
We need to know about the relation between the formation of an image and the position of the object for both the diverging and converging lenses. The diverging lens makes the light rays diverge and always form a virtual image, while a converging lens forms a real or virtual image based on the location of the object.

Complete step by step solution:
A concave or converging lens forms a virtual image when the object is placed at a distance less than one focal length. So, in case the object image has to be virtual, the focal length of the converging lens needs to be greater than the distance of the object from the lens, that is 15 cm.

While in case of a diverging lens, which diverges all the light rays passing to it, the image produced is always virtual irrespective of the distance of the object.

So, all the statements given are correct.

Hence, option d is the correct answer.

Additional Information:
We should know that for a converging lens, the position of the object determines whether the image will be real or virtual. There are certain positions to be considered if we want to know the location of the image formed.

For a converging lens, if the object is far from twice the focal length, the image formed will be real and in between the focal point and twice the focal distance. Similarly, by using a ray diagram, we can determine when the image will be real or virtual.

Note:
In only one case of the converging lenses, the image formed is virtual and in all other cases, the image is real. So, we need to be careful about choosing the correct option and should consider the position of the object given with respect to the lens.