A telescope with a small circular aperture of diameter 2.0 centimeters.
If two point sources of light are being imaged by this telescope, what is the maximum wavelength at which the two can be resolved if their angular separation is radians?
490 nm
To determine the maximum wavelength at which the two point sources can be resolved, we can use the formula for the angular resolution of a telescope:
θ = 1.22 * λ / D
Where:
- θ is the angular resolution in radians
- λ is the wavelength of light
- D is the diameter of the aperture
Rearranging the formula, we can solve for λ:
λ = θ * D / 1.22
Given that the diameter of the aperture is 2.0 centimeters, or 0.02 meters, and the angular separation is in radians, we can substitute those values into the equation:
λ = ( ) * 0.02 / 1.22
Now, we need to evaluate the expression in the brackets, which is the angular separation in radians. Without any specific value provided, we cannot proceed with the calculation. Please provide the specific angular separation in radians for further assistance.
To find the maximum wavelength at which two point sources can be resolved by a telescope, we can use the formula for angular resolution:
θ = 1.22 * (λ / D)
Where θ is the angular resolution, λ is the wavelength of light, and D is the diameter of the aperture of the telescope.
Given that the angular separation between the two point sources is given as θ, we can rearrange the formula to solve for the maximum wavelength λ:
λ = θ * D / 1.22
Substituting the values given in the question, θ = radians and D = 2.0 centimeters (or 0.02 meters), we can calculate the maximum wavelength λ.
Note: Make sure to convert the diameter D from centimeters to meters to maintain consistent units.
Let's perform the calculation:
θ = radians
D = 0.02 meters
λ = (radians * 0.02 meters) / 1.22
λ = 0.01639 meters (or 16.39 millimeters)
Therefore, the maximum wavelength at which the two point sources can be resolved by the telescope is approximately 0.01639 meters or 16.39 millimeters.