Stacy uses a close range telescope, which contains 2 converging lenses, each having a focal distance of 0.750 m, separated by a distance of 1.501 m. If she spots Jane, located a distance of 542 meters away, what is the magnification of the image she sees? is it upright or inverted>
Relevant equations
M=hi/ho
1/do + 1/di = 1/f
M= -di/do
To find the magnification of the image Stacy sees through her telescope, we can use the equation M = hi/ho, where M is the magnification, hi is the height of the image, and ho is the height of the object. However, since the question does not provide information about the height of the object, we need to use another equation to find the magnification.
For a telescope with two converging lenses, we can use the lens formula 1/do + 1/di = 1/f, where do is the object distance, di is the image distance, and f is the focal length of the lens.
Given that the focal length of each lens is 0.750 m and the lenses are separated by a distance of 1.501 m, we can determine the effective focal length of the telescope. Since the lenses are converging, their focal lengths will be positive.
1/f = 1/f1 + 1/f2
1/f = 1/0.750 + 1/0.750
1/f = 2/0.750
f = 0.375 m
Now, we can use the lens formula to find the image distance di.
1/do + 1/di = 1/f
1/542 + 1/di = 1/0.375
1/di = 1/0.375 - 1/542
1/di = (542 - 0.375 * 542) / (542 * 0.375)
1/di = (542 - 203.25) / 203.25
1/di = 338.75 / 203.25
1/di = 1.6667
di = 0.6 m
Now that we have determined the image distance, we can use the magnification equation M = -di/do to find the magnification.
M = -di/do
M = -0.6/542
M = -0.0011
The magnification of the image Stacy sees is -0.0011. Since the magnification is negative, the image is inverted.