How far apart are an object and an image formed by a 62 cm focal-length converging lens if the image is 2.75X larger than the object and is real?

Use the lens equation again. You should have memorized it by now.

Substitute 2.75 do for di and solve for image distance, di.

Distance from object to image = di + do = 3.75 di.

Mass spring system is hung vertically and set into oscllation Why does the motion eventually stops?

To solve this problem, we will use the lens formula, which relates the object distance (u), the image distance (v), and the focal length (f) of a lens. The lens formula is given by:

1/f = 1/v - 1/u

Given data:
Focal length (f) = 62 cm
Magnification (m) = 2.75 (since the image is 2.75X larger than the object)
Real image

To find the object distance (u) and image distance (v), we need to manipulate the lens formula.

1/u = 1/v - 1/f

Let's calculate the distances:

1/u = 1/v - 1/f

We know that the magnification (m) is given by:
m = -v/u

Since the image is larger than the object, the negative sign indicates that it's a real image.

Rearranging the magnification equation, we have:
-v/u = m

Substituting the given values, we get:
-1/v = 2.75

Now we can substitute this into the lens formula equation:

1/u = 1/v - 1/f

Substituting -1/v = 2.75:

1/u = 2.75 - 1/f

1/u = 2.75 - 1/62

Simplifying further, we get:

1/u = (2.75 * 62 - 1) / 62

1/u = (170.5 - 1) / 62

1/u = 169.5 / 62

Solving for u, we take the reciprocal of both sides:

u = 62 / 169.5

u ≈ 0.365 cm

So the object distance is approximately 0.365 cm.

Now that we have the object distance (u), we can find the image distance (v) using the magnification equation:

m = -v/u

Substituting the given magnification (m) of 2.75 and the object distance (u) of 0.365 cm:

2.75 = -v / 0.365

Rearranging the equation, we get:

v = -2.75 * 0.365

v ≈ -1 cm

The negative sign indicates that the real image is formed on the same side as the object (i.e., it's a real image).

So, the image distance (v) is approximately -1 cm.

To summarize, the object distance (u) is approximately 0.365 cm, and the image distance (v) is approximately -1 cm.