An object whose height is 0.670 meters is located 2.00 meters from the face of a thin convex lens with a focal length of 0.780 meters. The image will be located ______ meters away from the lens.

To find the location of the image formed by a thin convex lens, you can use the lens formula:

1/f = 1/v - 1/u

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

Given:
f = 0.780 meters (focal length of the lens)
u = 2.00 meters (distance of the object from the lens)

We need to find v, the distance of the image from the lens.

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

1/v = 1/f + 1/u

Now, substitute the given values:

1/v = 1/0.780 + 1/2.00

1/v = 1.282 + 0.500

1/v = 1.782

To solve for v, take the reciprocal of both sides:

v = 1/(1.782)

v ≈ 0.561 meters

Therefore, the image will be located approximately 0.561 meters away from the lens.