A concave mirror with a radius of curvature
of 1.7 m is illuminated by a candle located on
the symmetry axis 3.7 m from the mirror.
Where is the image of the candle?
Answer in units of m
To determine the position of the image of the candle, we can use the mirror equation:
1/f = 1/do + 1/di
where:
- f is the focal length of the mirror
- do is the object distance from the mirror (in this case, the distance of the candle from the mirror)
- di is the image distance from the mirror (the position we want to find)
In this case, we have a concave mirror, so the focal length is positive and given by:
f = R/2
where R is the radius of curvature of the mirror.
Given that the radius of curvature (R) is 1.7 m and the distance of the candle from the mirror (do) is 3.7 m, we can substitute these values into the equation:
1/f = 1/do + 1/di
1/(1.7/2) = 1/3.7 + 1/di
2/1.7 = 1/3.7 + 1/di
Now we can solve this equation to find the value of di, which represents the position of the image of the candle from the mirror.
1.176 = 0.270 + 1/di
1.176 - 0.270 = 1/di
0.906 = 1/di
di = 1 / 0.906
di ≈ 1.103 m
Therefore, the image of the candle is located approximately 1.103 m from the concave mirror.