An object of size 3cm is placed 14cm in front of a concave lens of focal length 21cm calculate position and size of the image?

To calculate the position and size of the image formed by a concave lens, you can use the lens formula and magnification formula.

The lens formula is given by:

1/f = 1/v - 1/u

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

The magnification formula is given by:

magnification (m) = -v/u

where m is the magnification, v is the image distance, and u is the object distance.

Let's calculate the position and size of the image using these formulas:

Given:
Object size (h) = 3 cm
Object distance (u) = -14 cm (since the object is placed in front of the lens, the distance is negative)
Focal length (f) = -21 cm (since it's a concave lens, the focal length is negative)

To find the image distance (v), we rearrange the lens formula as follows:

1/v = 1/f - 1/u
1/v = 1/-21 - 1/-14
1/v = -14/294 - 21/294
1/v = -35/294
v = -294/35

To find the magnification (m), we use the magnification formula:

m = -v/u
m = -(-294/35)/(-14)
m = -294/35 / -14
m = 294/490

Now, we can find the position and size of the image:

The position of the image is the distance of the image from the lens, so v = -294/35 cm.

The size of the image can be calculated using the magnification formula:
Size of the image (h') = magnification (m) * object size (h)
Size of the image = (294/490) * 3 cm

By evaluating the above expression, you can find the size of the image in centimeters.