A concave mirror has a radius of curvature of
1.61 m.
Calculate the position of the image produced
when an object is placed 2.66 m from
the mirror.
Answer in units of m.
Calculate the position of the image when an
object is placed 0.492 m from the mirror.
Answer in units of m.
To calculate the position of the image formed by a concave mirror, we can use the mirror formula:
1/f = 1/d_o + 1/d_i
Where:
- f is the focal length of the mirror
- d_o is the object distance (distance of the object from the mirror)
- d_i is the image distance (distance of the image from the mirror)
To find the position of the image for the given values, we need to first calculate the focal length of the mirror.
The formula to calculate the focal length of a concave mirror is:
f = R/2
Where:
- f is the focal length of the mirror
- R is the radius of curvature of the mirror
Given that the radius of curvature of the concave mirror is 1.61 m, we can calculate the focal length using the formula:
f = 1.61 m / 2 = 0.805 m
Now, let's calculate the position of the image for each given object distance.
1) When the object is placed 2.66 m from the mirror:
- d_o = 2.66 m
Using the mirror formula:
1/0.805 = 1/2.66 + 1/d_i
Simplifying the equation, we get:
d_i = 0.805 * 2.66 / (2.66 - 0.805) = 1.8062 m
Therefore, the position of the image is 1.8062 m from the mirror.
2) When the object is placed 0.492 m from the mirror:
- d_o = 0.492 m
Using the mirror formula again:
1/0.805 = 1/0.492 + 1/d_i
Simplifying the equation, we get:
d_i = 0.805 * 0.492 / (0.492 - 0.805) = -1.5235 m
Note that the negative sign indicates that the image is formed on the same side as the object (virtual image).
Therefore, the position of the image is -1.5235 m from the mirror.