In viewing through a magnifying glass, one usually positions one's eyes very close to the lens. Does angular magnification change if the eye is moved back?

The answer is yes, the angular magnification does change if you move your eye back from the magnifying glass, and it generally decreases.

Here's why:

The Key Factor: Eye Position

When using a magnifying glass optimally, you hold it close to your eye and position the object near the focal point of the lens. This creates a virtual, magnified image that appears at a comfortable viewing distance.

What happens when you move your eye back:

1. The viewing angle decreases - As you move away from the lens, you're viewing the virtual image from a greater distance. The image itself doesn't change size, but the angle it subtends at your eye becomes smaller, similar to how any object appears smaller when you move away from it.
2. You're essentially "wasting" magnification - The lens still creates the same magnified virtual image, but you're now observing it from farther away, reducing the angular size you perceive.

The Practical Effect

• Eye close to lens: Maximum angular magnification (this is why jewelers hold their loupes right up to their eye)
• Eye far from lens: Reduced angular magnification, though you might gain a wider field of view

This is why proper technique with a magnifying glass, microscope, or telescope eyepiece involves positioning your eye at the exit pupil - the optimal location very close to the lens where you get the full angular magnification the instrument is designed to provide.

So yes, keeping your eye close to the lens isn't just habit - it's essential for getting the maximum magnification!