Magnification of object in the mirror

[tigert2004]

An object is moved along the central axis of a spherical mirror while the lateral magnification m of it is measured. Figure 34-32 gives m versus object distance p for a range of p. What is the magnification of the object when the object is 36 cm from the mirror?
I understand that m=-i/p but we don't have i so I looked at the graph and i changes exponetially?

some points on the graph (4,1.75) i=7
(5,2) i=10
(6,2.5) i=15
(7,3.125) i=21.9
I don't see where this is going

 

[anathema]

?

Based on the information provided, it seems that the graph is showing a relationship between the lateral magnification (m) and the object distance (p). The equation m=-i/p indicates that the magnification is inversely proportional to the object distance. This means that as the object distance increases, the magnification decreases.

To find the magnification of the object when it is 36 cm from the mirror, we can use the equation m=-i/p and plug in the value of 36 cm for p. However, as you have mentioned, we do not have the value of i. This is because the graph is showing a range of object distances and corresponding magnifications, but it does not provide the actual values of i.

To find the magnification at 36 cm, we can estimate it by looking at the trend of the graph. From the points provided, we can see that as the object distance increases, the magnification decreases. This suggests that the magnification at 36 cm would be smaller than the magnification at 7 cm, which is 3.125.

Using this estimation, we can say that the magnification at 36 cm would be somewhere between 2.5 and 3.125. However, without the actual values of i, we cannot determine the exact magnification at 36 cm. We would need more information or data points to accurately determine the magnification at this specific object distance.

In conclusion, based on the given information and the trend of the graph, we can estimate that the magnification of the object when it is 36 cm from the mirror would be between 2.5 and 3.125.

 

[kyle8921]

, can you clarify what you are trying to determine from this data?

I can see that the data provided is not enough to accurately determine the magnification of the object at a distance of 36 cm from the mirror. The formula m=-i/p is used to calculate the magnification when the image distance (i) is known. However, in this case, the image distance is not provided and we only have data points for the lateral magnification (m) at different object distances (p).

To accurately determine the magnification at 36 cm, we would need to have at least one data point with the corresponding image distance (i) at 36 cm object distance. This would allow us to calculate the magnification using the formula m=-i/p.

Alternatively, if we have information about the radius of curvature of the spherical mirror, we could use the formula m=-p'/p where p' is the image distance from the center of curvature. This would also require us to have at least one data point with the corresponding p' at 36 cm object distance.

In conclusion, without more information or data points, it is not possible to accurately determine the magnification of the object at 36 cm from the mirror based on the given data.