Focal length of magnifying glass Why a magnifying glass has a short focal length? 
According to its work the object must be between the focus and the optical centre,  a large focal length will favour it,  then why is it so? 
 A: A magnifying glass is a double convex or converging lens. A lens is a curved transparent material that bends light. These lenses are used to produce a magnified image of an object. In the magnifying glass's lens there is a line that runs through the center of the lens and perpendicular to its surface it is called the principal axis. All light rays that enter parallel to the principal axis are refracted toward the focus, where they come together or converge. The distance from the focal point to the lens is called the focal length (ƒ). The reciprocal of the focal length is a measure of how strongly an optical system focuses or defocuses light.
The mathematical relationship that describes the behavior of all lenses is:
1/focal length = 1/distance from object to lens + 1/distance from image to lens
And that's how you measure the focal length of a magnifying glass.
Ref: https://hypertextbook.com/facts/2008/MonaZawam.shtml
A: The visual angle is the angle subtended by an object at the eye.
As the object gets closer to the eye the visual angle increases and so the image of the object on the retina of the eye becomes larger ie the object appears to be bigger.
If the object is too close to the eye, the eye cannot produce a sharp image on the retina.
The image of the object appears largest when it is placed at the near point of the eye which is assumed to be approximately $25\,\rm cm$ for a normal eye.  
A convex lens when used as a magnifying glass produces a virtual image of the object which subtends a larger visual angle than that produced by the object when looked at with the unaided eye.  
The ratio of the visual angle of the virtual image when using the magnifying to the visual angle of the object when viewed using the unaided eye is called the angular magnification $M$.  
For a lens of given focal length $f$ the greatest angular magnification is achieved when the image of the object when viewed through the magnifying glass is at the near point ie approximately $25\,\rm cm$ away from the eye and then $M = 1+ \dfrac{25\,\rm cm}{f\,\rm cm}$.  
So making the focal length shorter will increase the angular magnification, ie the image of the object will appear ti be larger, but at the same time could potentially limit the aperture of the lens.
