An astronomer wants to determine whether or not he or she can photograph Castor and Pollux at the same time on a 5 x 8 inch plate using a lens system with a 1200 mm focal length. If the two stars are approximately 5 degrees apart, will it be possible to make the photograph?
To determine whether it is possible to photograph Castor and Pollux at the same time on a 5 x 8 inch plate using a lens system with a 1200 mm focal length, we need to consider the angular separation and the field of view.
1. Find the angular separation: Given that the two stars are approximately 5 degrees apart, we have the angular separation.
2. Determine the field of view: The field of view is the extent of the observable universe through a given camera lens. To calculate it, we can use the formula:
Field of View = 2 * arctan (sensor size / (2 * focal length))
Here, the sensor size represents the dimension of the plate, which is 5 x 8 inches in this case, and the focal length is 1200 mm.
3. Compare the angular separation and the field of view: If the angular separation is smaller than the field of view, it means that both stars can be photographed within the frame. Otherwise, one or both of the stars may be outside the field of view.
Let's calculate the field of view and determine if it is possible to photograph both stars within the given parameters.
First, convert the sensor size from inches to millimeters:
5 inches = 127 mm (approximately)
8 inches = 203 mm (approximately)
Using the formula for field of view:
Field of View = 2 * arctan ((sensor size) / (2 * focal length))
Field of View = 2 * arctan ((127 mm) / (2 * 1200 mm))
Field of View = 2 * arctan (0.053)
Now, let's calculate the result:
Field of View ≈ 0.1 degrees
Comparing the angular separation of 5 degrees to the field of view of 0.1 degrees, we can see that the field of view is significantly smaller than the angular separation. Therefore, it will not be possible to photograph both Castor and Pollux within the frame using the given lens system and plate size.