If a concave mirror with a radius of curvature of 0.93 m has an object placed at 0.37 m in front of it, what is the mirror's focal length? Round your answer to 3 decimal places.
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To find the focal length of a concave mirror, you 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 (distance of the image from the mirror)
- u is the object distance (distance of the object from the mirror)
In this case, the object is placed at a distance of 0.37 m in front of the mirror. Therefore, u = -0.37 m (since the object is in front of the mirror, the distance is negative).
We also know that the radius of curvature (R) of the mirror is 0.93 m. For a concave mirror, the focal length (f) is half the radius of curvature. So, f = R/2.
Plugging these values into the mirror formula, we get:
1/f = 1/v - 1/u
1/f = 1/v - 1/(-0.37)
Simplifying further:
1/f = 1/v + 1/0.37
Now, we need to solve for v.
To find v, we can use the mirror magnification formula:
m = -v/u
Where m is the magnification. For this problem, we are not given the magnification, but we can assume it to be 1 (since it is not specified). Therefore, m = -1.
Plugging in the values, we get:
-1 = -v/0.37
Solving for v:
v = -0.37
Now, substituting v = -0.37 back into the equation:
1/f = 1/(-0.37) + 1/0.37
Simplifying further:
1/f = -2.703 + 2.703
1/f = 0
Since 1/f = 0, we can conclude that the focal length is infinite.
Therefore, the focal length of the concave mirror in this case is infinite.