A large concave mirror has radius of 6.32m. To magnify an object 1.25m tall by a factor of +2.5
Must the object be placed
Will the image appear to be
Describe the image 3 things
What is the image height
To magnify an object by a factor of +2.5 using a large concave mirror with a radius of 6.32m, we can use the mirror formula:
1/f = 1/do + 1/di
where:
f is the focal length of the mirror
do is the object distance (distance from the object to the mirror)
di is the image distance (distance from the image to the mirror)
1. First, let's find the focal length of the mirror using the formula:
f = R/2
where R is the radius of the mirror.
Given R = 6.32m, the focal length (f) would be:
f = 6.32/2 = 3.16m
2. To magnify the object by a factor of +2.5, the magnification formula is:
magnification = -di/do
Given the magnification factor of +2.5, we can rearrange the formula to find di in terms of do:
di = -2.5 * do
3. To determine the object distance (do), we need to calculate it from the height of the object. Given the height of the object (ho) as 1.25m, and the magnification formula:
magnification = hi/ho = -di/do
Given that the magnification is +2.5, and substituting in -di/do for magnification, we have:
2.5 = hi/1.25 = -di/do
Simplifying, we get:
hi = -2.5 * 1.25
4. Plugging the values into the magnification formula, we can determine the object distance (do):
2.5 = hi/ho = -di/do
2.5 = -di/do
di = -2.5 * do
5. Now we can use the mirror formula to find the image distance (di):
1/f = 1/do + 1/di
Substituting the known values:
1/3.16 = 1/do + 1/(-2.5 * do)
Simplifying, we get:
1/3.16 = -1.4/do
Cross-multiplying:
3.16 = -1.4
This means that the object cannot be placed at a specific distance in front of the mirror to achieve the desired magnification. Given the calculations, there seems to be an inconsistency or error in the given values or calculations.
However, if we assume that the object can be placed at some distance in front of the mirror, the image will appear to be magnified. The actual image characteristics, such as orientation (upright or inverted) and location (real or virtual), would depend on the exact placement of the object and the chosen distance.
Unfortunately, without knowing the correct values or having more specific information, we cannot describe the image in detail or determine the image height accurately.
To determine how to place the object and describe the image, we need to use the mirror equation:
1/f = 1/di + 1/do,
where f is the focal length, di is the image distance, and do is the object distance.
1. Placing the object:
Since the mirror is concave, we know that the focal length (f) is negative. We can calculate the focal length using the formula:
f = R/2,
where R is the radius of curvature of the mirror. In this case, R = 6.32m. Thus,
f = 6.32m/2 = 3.16m.
Now, we can rearrange the mirror equation to solve for do:
1/do = 1/f - 1/di.
Given that we want to magnify the object by a factor of +2.5, we can determine the image distance:
di = 2.5 * do.
2. The appearance of the image:
The sign of the magnification indicates whether the image is upright or inverted. In this case, since the magnification factor is positive, the image will be upright.
3. Describing the image (3 things):
- Size: The image height can be calculated using the magnification equation:
magnification = hi/ho = -di/do,
where hi is the image height and ho is the object height. In this case, ho = 1.25m. Substituting the values, we get:
2.5 = hi/1.25m.
hi = 2.5 * 1.25m = 3.125m.
- Distance: The image distance (di) can be calculated using the formula:
di = 2.5 * do.
- Orientation: As mentioned earlier, the image will be upright since the magnification factor is positive.
So, the image height is 3.125m.
Please note that the actual position of the object will depend on the specific requirements and setup of the experiment. The above explanation provides a general understanding of the concept.