The image formed by a concave mirror is: A.always real. B.always virtual. C.certainly real if the object is virtual. D.certainly virtual if the object is real.

To solve this question, let's analyze the properties of a concave mirror and its ability to form images based on the position of the object:

Concave Mirror: A concave mirror has a reflecting surface that curves inward. It is a converging mirror.

Image Formation: The type of image (real or virtual) depends on the object's position relative to the mirror:

If the object is placed beyond the focal point (F), the mirror forms a real and inverted image.
If the object is placed at the focal point (F), the reflected rays become parallel, and no image is formed.
If the object is placed between the focal point (F) and the mirror, the mirror forms a virtual and erect image.
Virtual Objects: A virtual object is an object formed by converging light rays or an image of another optical system. For a concave mirror, a virtual object will always produce a real image because the reflected rays converge to form it.

Now, consider the options:

A. Always real: This is incorrect because a concave mirror can form a virtual image if the object is placed between the focal point and the mirror.

B. Always virtual: This is incorrect because concave mirrors predominantly form real images for objects placed beyond the focal point.

C. Certainly real if the object is virtual: This is correct. A virtual object for a concave mirror always results in a real image.

D. Certainly virtual if the object is real: This is incorrect because real objects placed beyond the focal point form real images, not virtual ones.

Correct Answer: C. Certainly real if the object is virtual.