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.
Angular magnification (M) is the ratio of the angle subtended by the image (θ') to the angle subtended by the object (θ) when viewed through a lens. It can be calculated using the formula:
M = θ'/θ
To find the angle subtended by the object (θ) when viewed from Earth, we can use the following formula:
θ = size of the object / distance from the object
Given that the size of Jupiter is 1.43 x 10^5 km and the distance from Earth is 6.29 x 10^8 km, we can calculate θ.
θ = (1.43 x 10^5 km) / (6.29 x 10^8 km)
Now, let's substitute the values into the formula for angular magnification:
M = θ'/θ
To find θ', we can rearrange the formula as follows:
θ' = M * θ
Now, we need to find the value of θ' when the focal length of the lens is 9600 mm.
θ' = M * θ = M * (1.43 x 10^5 km) / (6.29 x 10^8 km)
To convert the angle from radians to degrees, multiply by 180/π.
θ' (in degrees) = (M * (1.43 x 10^5 km) / (6.29 x 10^8 km)) * (180/π)
Now, let's calculate the value of θ' using the given values:
θ' (in degrees) = (M * (1.43 x 10^5) / (6.29 x 10^8)) * (180/π)
This will give us the size of the image of Jupiter when photographed at opposition with a lens having a focal length of 9600 mm.