The convex lens of a copy machine has a focal length of 22.0 cm. A letter to be copied is placed 37.0 cm from the lens.

(a) How far from the lens is the copy paper?
(b) How much larger will the copy be?

To find the answers to these questions, we can use the lens formula for a convex lens:

1/f = 1/v - 1/u

Where:
- f is the focal length of the lens,
- v is the image distance (distance of the image from the lens), and
- u is the object distance (distance of the object from the lens).

Let's solve the problems step-by-step:

(a) How far from the lens is the copy paper?

In this case, the object distance (u) is given as 37.0 cm, and we need to find the image distance (v). The copy paper is located at the image distance from the lens.

1/f = 1/v - 1/u

Rearranging the equation to solve for v:

1/v = 1/f + 1/u

Substituting the known values:

1/v = 1/22.0 + 1/37.0

Now, solve for v:

1/v = (37.0 + 22.0) / (22.0 * 37.0)

1/v = 59.0 / (22.0 * 37.0)

v = (22.0 * 37.0) / 59.0

v ≈ 13.81 cm

Therefore, the copy paper is located approximately 13.81 cm from the lens.

(b) How much larger will the copy be?

To find the magnification of the lens, we can use the formula:

magnification (m) = -v / u

Where:
- v is the image distance (from part a),
- u is the object distance (given as 37.0 cm).

Substitute the values:

m = -13.81 cm / 37.0 cm

m ≈ -0.373

A negative sign indicates an inverted image.

Therefore, the copy will be approximately 0.373 times smaller than the original size.

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