A student obtains a blurred image of a distant object on a screen using a convex lens. To obtain a distinct image on the screen he should move the lens

For a convex lens, the position of the image ($v$) depends on the position of the object ($u$) according to the lens formula:

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

When a student obtains a blurred image of a distant object on a screen, it indicates that the screen is not positioned exactly at the image distance ($v$).

• If the screen is closer to the lens than the actual image distance, the lens needs to be moved away from the screen to focus the image.
• If the screen is further from the lens than the actual image distance, the lens needs to be moved towards the screen.

Since the exact position of the distant object determines where its sharp image will form, the lens must be moved either towards or away from the screen depending on the exact position of the object relative to the current setup.