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 find the position of the image of the candle formed by the concave mirror, we 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 from the mirror (positive for real images),
- u is the object distance from the mirror (positive for objects placed in front of the mirror).
In this case, the mirror is concave, so the focal length (f) is negative. The radius of curvature (R) is twice the absolute value of the focal length, so R = -2f = -1.22 m.
Given:
u = 2.61 m
R = -0.61 m
We need to find v, the image distance from the mirror. Rearranging the mirror formula, we can solve for v:
1/v = 1/f - 1/u
Substituting the known values:
1/v = 1/(-0.61) - 1/2.61
Now, we can calculate:
1/v = -1.639 - 0.383
1/v = -2.022
v = 1/(-2.022)
After evaluating, we find:
v ≈ -0.494 m
The negative sign indicates that the image is formed behind the mirror. Therefore, the image of the candle is approximately 0.494 m behind the concave mirror.