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 convex 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 of the mirror is given as 1.64 m. For a convex mirror, the focal length is half the radius of curvature:
f = R/2 where R is the radius of curvature.
Therefore, f = 1.64 m / 2 = 0.82 m.
The object distance (u) is given as 0.277 m.
Plugging these values into the mirror formula, we can solve for the image distance (v):
1/f = 1/v - 1/u,
1/0.82 = 1/v - 1/0.277.
Simplifying the equation:
1/v = 1/0.82 + 1/0.277,
1/v = (0.277 + 0.82)/(0.82 * 0.277).
Calculating the value:
1/v = 1.249/0.22794,
v = 0.22794/1.249.
v ≈ 0.182 m.
Therefore, the position of the image is approximately 0.182 m from the convex mirror.
To find the magnification, we can use the magnification formula:
magnification (m) = -v/u,
where v is the image distance and u is the object distance.
Plugging in the respective values:
m = -0.182/0.277,
Calculating:
m ≈ -0.656.
The magnification of the image formed by the convex mirror is approximately -0.656.