A convex mirror of radius of curvature 1.64 m is placed 0.277 m from a chess piece which is on the reflecting side of the mirror.
What is the position of the image? What is the magnification?
To determine the position of the image formed by the convex 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 distance of the image from the mirror, and
- u is the distance of the object from the mirror.
In this case:
- The radius of curvature (R) of the convex mirror is given as 1.64 m. Since the mirror is convex, the focal length is half the radius of curvature: f = R/2 = 1.64/2 = 0.82 m.
- The object distance (u) is given as 0.277 m.
Let's plug in these values into the mirror formula:
1/0.82 = 1/v - 1/0.277.
Simplifying this equation, we solve for v:
1/v = 1/0.82 + 1/0.277,
1/v = (1.2134 + 3.6079)/0.82,
1/v = 4.8213/0.82,
1/v = 5.8776,
v = 1/5.8776,
v ≈ 0.17 m.
Therefore, the image formed by the convex mirror is located approximately 0.17 m from the mirror on the reflecting side.
To find the magnification, we can use the formula:
magnification (m) = -v/u,
where:
- v is the distance of the image from the mirror, and
- u is the distance of the object from the mirror.
Plugging in the given values:
m = -(0.17 m) / (0.277 m),
m ≈ -0.613.
The negative sign indicates that the image formed by the convex mirror is virtual and upright.
To summarize:
- The position of the image is approximately 0.17 m from the convex mirror on the reflecting side.
- The magnification is approximately -0.613, indicating that the image is virtual and upright, and the size of the image is reduced.