A concave mirror with a radius of curvature
of 0.61 m is illuminated by a candle located
on the symmetry axis 2.61 m from the mirror.
Where is the image of the candle?
Answer in units of m.
To determine the position of the image formed by a concave mirror, we can use the mirror formula:
1/f = 1/d0 + 1/di
Where:
- f is the focal length of the mirror,
- d0 is the object distance (distance of the candle from the mirror), and
- di is the image distance (distance of the image from the mirror).
Given data:
- Radius of curvature (R) = 0.61 m
- Object distance (d0) = 2.61 m
First, we need to find the focal length (f) of the mirror. For a concave mirror, the relationship between the radius of curvature and the focal length is:
f = R/2
Substituting the given radius of curvature, we can find:
f = 0.61 m / 2 = 0.305 m
Now, we can use the mirror formula to find the image distance (di):
1/0.305 = 1/2.61 + 1/di
Simplifying this equation gives us:
di = 0.115 m
Therefore, the image of the candle is located at a distance of 0.115 m from the mirror.