An object be placed at an unknown distance from a convex lens of focal length 20 cm to obtain its real image at a distance of 30 cm from the lens. What will be the height of the image if the object is 6 cm tall?

To find the height of the image formed by a convex lens, we can use the lens formula:

1/f = 1/v - 1/u

Where: f = focal length of the lens v = distance of the image from the lens u = distance of the object from the lens

Given: f = 20 cm v = 30 cm

We need to find the distance of the object from the lens (u) in order to calculate the height of the image.

Using the lens formula, we can rearrange it to solve for u:

1/u = 1/f - 1/v

Substituting the given values:

1/u = 1/20 - 1/30

Simplifying the equation:

1/u = (3 - 2)/60

1/u = 1/60

Therefore, u = 60 cm.

Now that we know the distance of the object from the lens (u), we can use the magnification formula to find the height of the image:

magnification (m) = height of the image (h') / height of the object (h)

The magnification formula is given by:

m = -v/u

Substituting the given values:

m = -30/60

Simplifying the equation:

m = -1/2

Since the magnification is negative, it indicates that the image formed is inverted.

Now, we can find the height of the image (h'):

m = h'/h

-1/2 = h'/6

Simplifying the equation:

h' = -3 cm

Therefore, the height of the image formed by the convex lens will be -3 cm, indicating that it is inverted and 3 cm in height.