A real object is located at the zero end of a meter stick. A large concave mirror at the 100 cm end of the meter stick forms an image of the object at the 72.5 cm position. A small convex mirror placed at the 20.6 cm position forms a final image at the 10.0 cm point. What is the radius of curvature of the convex mirror?

1/F = 1/(72.5-20.6)+1/(-(20.6-10))

-> F = -13.3
-> C = -26.6

Good luck with your Physics exam :)

To determine the radius of curvature of the convex mirror, we can use the mirror formula:

1/f = 1/v - 1/u,

where:
- f is the focal length of the mirror,
- v is the image distance,
- u is the object distance.

In this case, we have the image formed by the concave mirror at the 100 cm position. Therefore, the object distance for the convex mirror would be the distance between the concave mirror and the convex mirror, which is given by:

u = 100 cm - 20.6 cm = 79.4 cm.

Additionally, we are given that the final image is formed at the 10.0 cm point. So, the image distance would be:

v = 10.0 cm.

Now, we can substitute these values into the mirror formula to solve for the focal length of the convex mirror:

1/f = 1/v - 1/u
1/f = 1/10 - 1/79.4.

Simplifying this equation and finding the inverse will give us the desired result:

f = 15.59 cm.

Since the radius of curvature (R) of a spherical mirror is simply twice the focal length (f), we can conclude that the radius of curvature of the convex mirror is:

R = 2f = 2 * 15.59 cm = 31.18 cm.

To find the radius of curvature of the convex mirror, we can use the mirror equation:

1/f = 1/di + 1/do,

where:
- f is the focal length of the mirror,
- di is the image distance from the mirror, and
- do is the object distance from the mirror.

Step 1: Find the object distance from the convex mirror.
The object distance, do, is the distance between the convex mirror and the final image position. From the given information, the final image is formed at the 10.0 cm point, which means the object is located at the 72.5 cm position with respect to the concave mirror. Using the meter stick as reference, the object distance for the convex mirror is:
do = 72.5 cm + 20.6 cm = 93.1 cm.

Step 2: Find the image distance from the convex mirror.
The image distance, di, is the distance between the convex mirror and the final image position. From the given information, the final image is formed at the 10.0 cm point. Therefore, the image distance is:
di = 10.0 cm.

Step 3: Solve for the focal length of the convex mirror.
Now that we have the object and image distances, we can substitute them into the mirror equation to solve for the focal length, f.
1/f = 1/di + 1/do
1/f = 1/10.0 cm + 1/93.1 cm
1/f = 0.1 cm^-1 + 0.0107655 cm^-1
1/f = 0.1107655 cm^-1

Taking the reciprocal of both sides, we get:
f = 8.3 cm^-1.

Step 4: Find the radius of curvature of the convex mirror.
The radius of curvature, R, is related to the focal length, f, by the equation:
1/f = 2/R.

Using this equation, we can solve for the radius of curvature:
1/f = 2/R
1/8.3 cm^-1 = 2/R

Taking the reciprocal of both sides, we get:
8.3 cm^-1 = R/2

R = 1 / (8.3 cm^-1/2)
R = 1 / 4.15 cm^-1
R = 0.241 cm.

Therefore, the radius of curvature of the convex mirror is approximately 0.241 cm.