Consider a compound microscope that has a minimum separation angle of
0.5 ¦Ìrad when it satisfies the ¡®just resolved¡¯ condition. When its objective lens
with a circular aperture is immersed in oil whose refractive index is 1.53,
determine the limiting angle of resolution.
To determine the limiting angle of resolution, we need to use Rayleigh's criterion. Rayleigh's criterion states that two objects are just resolved when the maximum of one Airy disk falls on the first minimum of the other Airy disk.
The formula for the limiting angle of resolution (θ) is given by:
θ = 1.22 * (λ / D)
Where:
- θ is the limiting angle of resolution,
- λ is the wavelength of light used,
- D is the diameter of the aperture of the objective lens.
In this case, we need to determine the limiting angle of resolution for a compound microscope with an object lens immersed in oil whose refractive index is 1.53.
Here's how we can proceed:
Step 1: Calculate the wavelength of light used.
The wavelength of light used is not given in the problem statement. You will need to have this information in order to calculate the limiting angle of resolution.
Step 2: Determine the diameter of the aperture of the objective lens.
The diameter of the aperture of the objective lens is not provided in the problem statement. You will need to obtain this information in order to calculate the limiting angle of resolution.
Step 3: Use the formula to calculate the limiting angle of resolution.
Using the values for the wavelength of light (λ) and the diameter of the aperture (D) obtained in steps 1 and 2, respectively, you can now calculate the limiting angle of resolution using the formula θ = 1.22 * (λ / D).
Please note that without the values for the wavelength of light and the diameter of the aperture, it is not possible to calculate the limiting angle of resolution. You will need to obtain these values in order to proceed with the calculation.