(a) Upper half of a convex lens is covered with a black paper. Draw a ray diagram to show the formation of image of an object placed at a distance of 2F from such a lens. Mention the position and nature of the image formed. State the observable difference in the image obtained if the lens is uncovered. Give reason to justify your answer.

(b) An object is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 15 cm. Use lens formula to determine the distance of the image from the optical centre of the lens.

(a) When the upper half of a convex lens is covered with a black paper, the light rays coming from the object placed at a distance of 2F will pass through the lower half of the lens. The ray diagram will be as follows:

The image formed will be at a distance of 2F from the lens, real and inverted.

If the lens is uncovered, the image will be brighter and more intense because more light rays will be able to pass through the lens.

(b) Given that the object distance (u) is 30 cm and the focal length (f) is -15 cm (negative sign for concave lens), we can use the lens formula to determine the image distance (v):

\(\frac{1}{v} = \frac{1}{f} - \frac{1}{u}\)

\(\frac{1}{v} = \frac{1}{-15} - \frac{1}{30}\)

\(\frac{1}{v} = \frac{-2-1}{30}\)

\(\frac{1}{v} = \frac{-3}{30}\)

\(\frac{1}{v} = \frac{-1}{10}\)

v = -10 cm

The image distance is -10 cm, which means the image is virtual and located 10 cm from the lens on the same side as the object.