We say that concave mirrors when form inverted image then that image is real but when we see in front of spoon from inward side from some distance then it will form inverted image but we don't place any screen in front of spoon. We will observe tht image will form on surface of spoon but real image is not formed on mirror. Why that is so?Is the image formed virtual?But concave mirror forms vitual image but erect.

Concave mirrors form real and inverted image when the object is placed at focus or beyond it. 

When we place the spoon in front of our eye, the distance of our face from the surface of spoon is more than focal length of the spoon.

Hence, the concave mirror should form real and inverted image of our face.

 

Now, according to you there is no screen in front of our spoon. This is incorrect as the retina of our eye acts as a screen. 

Hence, the image of our face is formed on the screen which makes it a real image and not a virtual image.