What is the relation of resolution with linear and angular magnification of a convex lens?

1) Linear magnification is the ratio of size of image to the size of object located at same distance. Whereas angular magnification is the ratio of Visual angle subtended by image at an aided eye to visual angle subtended by object at unaided or naked eye. which of them is related to resolution? 2) On optical devices which magnification is mentioned linear or angular?

2 Answers

Resolution is to do with an optical instrument obstructing wavefronts and hence causing diffraction effects.

For example, a telescope with diameter of lens/mirror $D$ the smallest angular separation $\theta$ which can be resolved at a wavelength $\lambda$ is given by $\theta = 1.22 \frac \lambda D$.
However for microscopes resolution is often quoted in terms is the smallest distance between two objects which can be resolved.

A lot/most? optical instruments are capable of producing a final image at infinity even though that may not produce the maximum angular magnification.
This is because when the eye is used to make observations it will not fatigue as quickly as compared with having the final image at the near point.
If the final image is at infinity then the only measure of magnification which is sensible is angular magnification.
So when a telescope manufacturer quotes the magnification as $50\times$ it is an angular magnification which is quoted with the final image at infinity.

Increasing magnification does not increase resolution, all that happens is that the diffraction patterns just get bigger and that does not improve the ability to resolve two objects.

In fact linear or angular magnification has nothing to do with resolution. You can have a device with large resolutions but poor magnification. To be of use resolution is increased so that the increased magnification can be useful. Resolution is related to the aperture size as given by the formula by Farcher.