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 produced by a concave mirror, you can use the mirror equation, which is given by:
1/f = 1/do + 1/di
where:
- f is the focal length of the mirror,
- do is the object distance (distance between the object and the mirror), and
- di is the image distance (distance between the image and the mirror).
In this case, the radius of curvature (R) of the mirror is given as 1.61 m. The focal length (f) of the mirror can be calculated using the formula:
f = R/2
Let's calculate the focal length first:
f = 1.61 m / 2
f = 0.805 m
Now, we can substitute the values into the mirror equation and solve for di:
1/0.805 = 1/2.66 + 1/di
Rearrange the equation to solve for di:
1/di = 1/0.805 - 1/2.66
Now, calculate the inverse of the right-hand side of the equation:
1/di = (2.66 - 0.805) / (0.805 * 2.66)
Finally, find di by taking the inverse of both sides:
di = 1 / (2.66 - 0.805) / (0.805 * 2.66)
Evaluate the expression to find the position of the image:
di = 1.0787 m
Therefore, the position of the image produced by the concave mirror when the object is placed 2.66 m from the mirror is approximately 1.0787 m.