A convex lens of focal length 6cm is held 4cm from a newspaper, which has print 0.5cm high.By calculation, determine the size and nature of the image produced.

To determine the size and nature of the image produced by the convex lens, we can use the lens formula:

1/f = 1/v - 1/u

where f is the focal length of the lens, v is the image distance, and u is the object distance.

Given that the focal length of the lens is 6cm and the object distance is 4cm, we can substitute these values into the lens formula:

1/6 = 1/v - 1/4

To solve for v, we can rearrange the equation:

1/v = 1/6 + 1/4

Combining the fractions:

1/v = (2 + 3)/12

1/v = 5/12

Now, we can find the value of v:

v = 12/5

v = 2.4 cm

So, the image distance is 2.4 cm.

To determine the size of the image, we can use the magnification formula:

magnification = height of image / height of object = v/u

Given that the height of the object (newspaper print) is 0.5 cm and the object distance is 4 cm, we can substitute these values into the magnification formula:

magnification = 2.4 / 4

magnification = 0.6

So, the magnification is 0.6.

To find the height of the image, we can multiply the magnification by the height of the object:

height of image = magnification * height of object

height of image = 0.6 * 0.5

height of image = 0.3 cm

Therefore, the size of the image produced by the convex lens is 0.3 cm and it is a reduced image (since the magnification is less than 1).