A microscope is an optical instrument used to view objects that are too small to be seen by the naked eye. It magnifies small objects using a system of lenses, allowing scientists, researchers, and students to observe microscopic structures in detail. Microscopes are essential tools in biology, medicine, materials science, and many other fields.

Two key formulas are used in microscopy calculations:

\[ M_{total} = M_{objective} \times M_{eyepiece} \]

Where:

- \( M_{total} \) is the total magnification
- \( M_{objective} \) is the magnification of the objective lens
- \( M_{eyepiece} \) is the magnification of the eyepiece

\[ R = \frac{0.61\lambda}{NA} \]

Where:

- \( R \) is the resolution (in micrometers, μm)
- \( \lambda \) is the wavelength of light (in micrometers, μm)
- \( NA \) is the numerical aperture of the objective lens

Let's calculate the total magnification and resolution for a microscope:

- Given:
- Objective lens magnification = 40x
- Eyepiece magnification = 10x
- Numerical aperture (NA) = 0.65
- Wavelength of light = 550 nm (0.55 μm)

- Calculate total magnification: \[ M_{total} = M_{objective} \times M_{eyepiece} = 40 \times 10 = 400x \]
- Calculate resolution: \[ R = \frac{0.61\lambda}{NA} = \frac{0.61 \times 0.55 \text{ μm}}{0.65} \approx 0.52 \text{ μm} \]

Let's visualize the components of a microscope:

This diagram illustrates:

- The eyepiece (green circle) at the top
- The objective lens (yellow circle) near the bottom
- The specimen (teal rectangle) at the base
- The light path (gray dashed line) from the specimen through the lenses
- The body tube (red rectangle) connecting the eyepiece and objective

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