The distance between a concave mirror and an object placed I front of it is 1•0m. If the radius of curvature of the minor is 4•0m, the image formed will be?
To determine the type and properties of the image formed, we can use the mirror equation:
1/f = 1/v - 1/u,
where f is the focal length of the mirror, v is the image distance, and u is the object distance.
Given:
u = 1.0 m,
f = R/2 = 4.0 m / 2 = 2.0 m.
By substituting these values into the mirror equation, we can solve for the image distance:
1/2.0 = 1/v - 1/1.0.
1/2.0 = 1/v - 1.
1/v = 1 - 1/2.0 = 1/2.0.
v = 2.0 m.
Therefore, the image distance is v = 2.0 m.
To determine the type of image formed, we can now use the magnification equation:
m = -v/u,
where m is the magnification.
m = -2.0/1.0 = -2.0.
Since the magnification is negative, the image formed by the concave mirror is real, inverted, and diminished.
To determine the image formed by a concave mirror when an object is placed in front of it, we can use the mirror formula:
1/f = 1/v - 1/u
where:
f is the focal length of the concave mirror
v is the image distance from the mirror
u is the object distance from the mirror
First, let's determine the focal length of the concave mirror using the radius of curvature (R):
f = R/2 = 4/2 = 2 meters
Given:
u = -1.0 meters (the object distance)
f = 2 meters (the focal length)
Now, let's substitute the values into the mirror formula and solve for v:
1/2 = 1/v - 1/-1.0
To simplify the equation, we multiply both sides by 2:
1 = 2/v + 2
Subtracting 2 from both sides:
-1 = 2/v
Dividing both sides by -1:
1/v = -1/2
Taking the reciprocal of both sides:
v = -2/1
Therefore, the image distance (v) is -2 meters.
The negative sign indicates that the image formed by the concave mirror is virtual and located behind the mirror. The magnitude of the image distance (|v|) is 2 meters.
To determine the type and characteristics of the image formed in a 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 (distance between the mirror and the image)
- u is the object distance (distance between the mirror and the object)
In this case, the radius of curvature of the mirror is given as 4.0 m. Now, we know that the focal length (f) is half the radius of curvature:
f = r/2 = 4.0 m / 2 = 2.0 m
The object distance (u) is given as 1.0 m.
Substituting the known values into the mirror formula:
1/2.0 = 1/v - 1/1.0
Simplifying the equation gives:
1/2.0 = 1/v - 1
Now, let's find the common denominator and rearrange the equation:
2/2.0 = 2/v - 1
1 = 2/v - 1
Adding 1 to both sides of the equation:
2 = 2/v
Dividing both sides of the equation by 2:
v = 1.0 m
The image distance (v) is 1.0 m.
Since the image distance (v) is positive, the image formed by the concave mirror is real. Furthermore, since the object distance (u) is less than the focal length (2.0 m), the image formed is magnified and inverted.
Therefore, the image formed by the concave mirror will be real, magnified, and inverted.