In a modern optical measuring microscope, the 'cross-wires' are:

Explanation:

Correct Option: Etched on Glass within the Eyepiece

In a modern optical measuring microscope, the 'cross-wires' are indeed etched on glass within the eyepiece. This design allows for precise and accurate measurement and alignment. The eyepiece, also known as the ocular lens, is the part of the microscope that you look through to see the magnified image of the specimen. Within the eyepiece, a reticle (or graticule) is etched on a piece of glass. This reticle usually consists of cross-wires or a grid, which helps in measuring and positioning the specimen accurately.

Having the cross-wires etched on glass within the eyepiece offers several advantages:

• Precision: The etched reticle provides a fixed reference point, ensuring that measurements are consistent and precise every time.
• Durability: The reticle is protected within the eyepiece and is less prone to damage or wear compared to other locations.
• Ease of Use: The user can easily align and measure the specimen without any additional setup, as the cross-wires are always in view when looking through the eyepiece.

The reticle's design can vary depending on the microscope's intended use. For instance, some reticles may feature a simple cross-hair design, while others might have a more complex grid or scale pattern for detailed measurements.