Predict the size of the image of Jupiter if photographed at opposition with a lens having a focal length of 9600 mm. (Assume Jupiter is a disk of 1.43 x 10^5 km and is 6.29 x 10^8 km from the Earth.)
To predict the size of the image of Jupiter when photographed at opposition with a lens having a focal length of 9600 mm, we can use the concept of angular magnification.
The angular magnification is given by the formula:
M = -f / (D - f)
Where,
M is the angular magnification,
f is the focal length of the lens, and
D is the distance between the object and the lens.
In this case, the object is Jupiter, which is located 6.29 x 10^8 km from Earth. The focal length of the lens is 9600 mm, which can be converted to meters by dividing it by 1000 (9600 mm / 1000 = 9.6 m).
Substituting the values into the formula, we get:
M = -9.6 / (6.29 x 10^8 - 9.6)
Now we can calculate the angular magnification:
M = -9.6 / (6.29 x 10^8 - 9.6)
M = -9.6 / 6.2899904 x 10^8 (rounded to the same number of significant figures as the given values)
The angular magnification gives us the ratio between the apparent size of the image and the actual size of the object.
To find the size of the image, we multiply the angular magnification by the size of the object. The apparent size of the image is:
Size of the image = M * size of Jupiter
Size of the image = M * 1.43 x 10^5 km (rounded to the same number of significant figures as the given values)
Substituting the calculated value of M:
Size of the image = (-9.6 / 6.2899904 x 10^8) * 1.43 x 10^5 km
Now we can calculate the size of the image of Jupiter when photographed at opposition using the given values.