Why image formation requires a screen? what is exactly happening at atomic level when image is formed on a screen? why image can not be formed without screen. can someone explain intuitively.
 A: Rays of light for a point O on an object converge to a point I, the real image of O. But what do the rays do then? Without a screen, they carry on straight, forming a narrow cone of rays diverging from I and still going away from the lens. If you are on the lens side of the image you won't see it because the light isn't coming your way. If, though, you put a screen where the image is formed, light is scattered back from I towards you.
Scattering from the screen is due to electrons in atoms very near the screen's surface that are 'perturbed' by the electric field of the incident light. They are made to oscillate at the same frequency as the light, but the oscillating electrons re-emit radiation of the same frequency, but not in one unique direction. So if you can be almost anywhere on the lens side of the screen, and you will see light scattered from the point on the screen at I. [If the screen were not a matte surface, but were properly flat then there would be re-inforcement of emitted rays at one particular 'angle of reflection.]
You might be thinking: suppose there were no screen and you (the viewer) were on the other side of I to the lens. Wouldn't you see I because you receive the rays diverging out from I (see first paragraph)? Possibly, but your eye would have to be in the right place to intercept that narrow cone of rays. And it won't just be rays from I that you need to receive: the object will be extended, consisting of many points, and so will the image! If your eye is in the right place to receive light from some of these points, it won't receive light from others.
A: Images do not need to be formed on a screen.
An image looks like an object because rays of light come from an image the same way (more or less) as they come from an object.  Sometimes an image is formed on a screen and then rays of light come from a screen in the same way as the come from an object there are other types of images that we can see.  A regular bathroom mirror, for example, produces a virtual image with no screen involved.  We can also see real images without screens.  For example, if you look through a magnifying glass (convex lens) at a distant object you will see an inverted real image.  Unlike a virtual image, you could project this image on a screen and see it but you can also see it just by looking through the lens.
Now, some people may argue that we only ever see real images in the sense that real images are formed on our retinas.  If you want to call the retina a screen then I am forced to agree with you that an image can not be formed, or at least seen, without a screen.  If you want to know how retina detects light and an image is formed in the brain then you should rephrase you question.
