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 using a lens with a focal length of 9600 mm, we can use the following formula:
Image size = Object size × (focal length / object distance)
Where:
- Image size is the size of the image formed on the camera sensor or film,
- Object size is the actual size of the object being photographed,
- Focal length is the focal length of the lens being used, and
- Object distance is the distance between the object and the camera (in this case, the distance between Earth and Jupiter).
First, let's convert the given values for Jupiter's size and distance to meters to maintain consistent units:
Jupiter's size = 1.43 x 10^5 km = 1.43 x 10^8 meters
Object distance = 6.29 x 10^8 km = 6.29 x 10^11 meters
Now, we can substitute these values into the formula:
Image size = 1.43 x 10^8 × (9600 / 6.29 x 10^11)
Next, let's calculate this expression:
Image size ≈ 0.00349649227 meters (or approximately 3.5 millimeters)
Therefore, the predicted size of the image of Jupiter, when photographed at opposition with a lens having a focal length of 9600 mm, is approximately 3.5 millimeters.