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[Music] hi im adam this is the machine tech video blog and today im going to continue our discussion on auto collimators in the previous video i described in a very general sense how auto collimators work including why they are only sensitive to angular changes in a mirror and why thats so useful i also casually mentioned that based on the focal length of the objective lens in the auto collimator as well as on the resolution of the scale and the magnification of the eyepiece both of which have to do with sensing the movement of the return image of the crosshair you can tell exactly what the angular change of that mirror is very very precisely in this video were going to explore those relationships further which means were going to have to dig even deeper into optics and the related math but dont worry im going to try to cover this as intuitively as i possibly can and luckily all of the parameters i just described are related through a very simple formula the autocollimator form

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What is lateral resolution formula?

Lateral resolution is approximated by the 6 dB full-width half-maximum beam profile, given by LR = 0.4 F/L, where LR is the lateral resolution, is the ultrasound wavelength, F is the focal depth, and L is the active aperture length [20]. So, the greater the aperture, the better the LR.

Where does the 1.22 come from in electron diffraction?

If you are wondering about the 1.22 prefactor, it comes from the first node of a Bessel function.

Where does the 1.22 come from in the formula for angular resolution?

Its hard to tell exactly what you are asking because if you have followed the derivation then the answer is there: 1.22 is where the Bessel function has the first zero, and the Bessel function arises from the Fourier transform of the aperture function.

Why is there a diffraction limit?

The limit is basically a result of diffraction processes and the wave nature of light. The high frequency components that give an image its sharpness are lost by the finite numerical aperture of the lens that collects the light. This results in a blurry appearance of the captured image.

What is 1.22 wavelength D?

The Rayleigh criterion stated in the equation =1.22D = 1.22 D gives the smallest possible angle between point sources, or the best obtainable resolution. Once this angle is found, the distance between stars can be calculated, since we are given how far away they are.

What is the formula for resolving power?

The resolving power of the microscope is Xmin = 1.22/ numerical aperture. The resolving power depends on the aperture of the objective and the wavelength of light.

Why is 1.22 diffraction limit?

The factor of 1.22 applies to circular apertures like the pupil of your eye or the apertures in telescopes and cameras. When light passes through an aperture with diameter D, then diffraction limits the resolution to = 1.22/D. If the angular separation of two sources is less than , they cannot be resolved.

What is the formula for resolution of microscope?

d = /(2NA) where is the wavelength of light used to image a specimen. If using a green light of 514 nm and an oil-immersion objective with an NA of 1.45, then the (theoretical) limit of resolution will be 177 nm.

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