A dime .334 m away from, and on the optical axis of, a concave spherical mirror produces an image on the same side of the mirror as the source. The image is .093 m away from the mirror. If the dime is moved on the axis to .229 m from the mirror, how far away from the mirror is the image now?
What is the radius of the sphere of which the mirror is a section?
i still need to know how to find the radius
Use the mirror equation I provided in my previous answer
1/Do + 1/Di = 1/f = 2/R
Solve that for R. You won't need to solve for the focal length f.
To find the radius of the sphere of which the concave mirror is a section, we can use the mirror equation. The mirror equation relates the distance of the object (d_o) to the distance of the image (d_i) and the focal length of the mirror (f):
1/f = 1/d_o + 1/d_i
In this case, we know the initial distance of the object (d_o) from the mirror is 0.334 m, and the distance of the image (d_i) is 0.093 m.
Substituting these values into the mirror equation, we get:
1/f = 1/0.334 + 1/0.093
Simplifying this equation will give us the value of 1/f. Once we find 1/f, we can calculate the radius (R) of the mirror using the formula:
R = 2f
Now let's calculate it step by step:
Step 1: Calculate 1/f:
1/f = 1/0.334 + 1/0.093
= (0.093 + 0.334)/(0.334 * 0.093)
= 5.631/0.031002
≈ 181.57
Step 2: Calculate f:
1/f = 1/181.57
f = 1/(1/181.57)
f ≈ 0.0055 m
Step 3: Calculate R:
R = 2f
R = 2 * 0.0055
R ≈ 0.011 m
Therefore, the radius of the sphere of which the mirror is a section is approximately 0.011 meters (or 11 millimeters).