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Explain Bot To estimate the magnification and focal length of the pitcher of water shown in the figure, we can use the thin lens formula and the magnification formula.
1. Magnification (m):
The magnification (m) can be calculated using the formula:
m = -h'/h
where h' is the height of the inverted image and h is the height of the object.
In this case, the height of the tree is given as 42 ft, and its inverted image height is given as 1 ft. Substituting these values into the formula:
m = -1/42
Thus, the magnification is approximately -0.0238 (negative sign indicates inversion).
2. Focal length (f):
The focal length can be estimated using the lens formula:
1/f = 1/d_o + 1/d_i
where d_o is the object distance and d_i is the image distance.
In this case, the object distance is given as 220 ft, and the image distance can be taken as the distance between the pitcher and the image formed by the lens (based on the assumption that the pitcher acts as a diverging lens and forms a virtual image). From the given diagram, it appears that the image distance (d_i) is the distance between the pitcher and the image.
Hence, substituting the given values:
1/f = 1/220 + 1/d_i
Since we do not have the value of d_i, we cannot calculate the exact focal length. However, we can estimate the value based on the diagram or additional assumptions.
Please note that the given image link is not accessible; therefore, the exact values cannot be determined without visual reference.