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
what is the answer
To find the image of the candle formed by the concave mirror, we can use the mirror equation:
1/f = 1/do + 1/di
Where:
- f is the focal length of the mirror (which can be calculated using f = R/2, where R is the radius of curvature)
- do is the object distance (the distance between the object and the mirror)
- di is the image distance (the distance between the image and the mirror)
Given:
- Radius of curvature (R) = 0.61 m
- Object distance (do) = 2.61 m
First, let's find the focal length (f) using f = R/2:
f = 0.61 m / 2
f = 0.305 m
Now, we can plug these values into the mirror equation and solve for the image distance (di):
1/0.305 = 1/2.61 + 1/di
1/di = 1/0.305 - 1/2.61
1/di = (2.61 - 0.305) / (0.305 × 2.61)
1/di = 2.305 / 0.79705
di = 0.79705 / 2.305
di ≈ 0.346 m
Therefore, the image of the candle formed by the concave mirror is located at approximately 0.346 m from the mirror.