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In the world of optics, magnification quantifies how much larger an object appears when viewed through an optical instrument, such as a compound microscope. A compound microscope uses two lenses to magnify the image of a small specimen. The total magnification is the product of the magnification of its individual lenses: the objective lens and the eyepiece. In our problem, the total magnification of the microscope is 30. This indicates how many times larger the image appears compared to the actual object. Mathematically, we express total magnification as:

• \[ M = M_o \times M_e \]

where \( M \) is the total magnification, \( M_o \) is the magnification of the objective lens, and \( M_e \) is the magnification of the eyepiece.
The greater the magnification, the more detail we can see in the tiny structures of the specimen, allowing for a deeper understanding of its physical properties.

The least distance of distinct vision, often denoted as \( D \), is the minimum distance at which the human eye can focus on an object without strain. Generally, this distance is around 25 cm for a person with normal vision.
In the context of microscopy, knowing the least distance of distinct vision helps determine where to position the image formed by a microscope for comfortable viewing. This distance is crucial when calculating the eyepiece magnification, using the formula:

• \[ M_e = 1 + \frac{D}{f_e} \]

where \( f_e \) is the focal length of the eyepiece. It ensures that the observer can view the magnified image clearly without eye strain.

Focal length is a term used in optics to describe the distance from the lens's center to its focal point, where parallel rays of light converge. It is crucial in determining how much an object is magnified when viewed through a lens.
For a microscope, each lens—objective and eyepiece—has its own focal length, affecting the total magnification of the instrument. The shorter the focal length, the greater the potential magnification because the lens bends light more sharply.
In our exercise, the eyepiece has a focal length of 5 cm. This parameter is used in calculating the eyepiece magnification (\( M_e \)), influencing the overall magnification when combined with the objective lens.

The objective lens is one of the primary lenses in a compound microscope. Positioned close to the specimen, it is responsible for the initial magnification and focusing of the image.
Different objective lenses offer varying levels of magnification, and they work in tandem with the eyepiece to achieve the total desired magnification. In many microscopes, objective lenses can be switched to adjust the level of detail observed.

• Low power lenses for general overviews.
• High power lenses for detailed analysis.

For our specific problem, the task was to find the magnification by the objective lens when the image is viewed at the least distance of distinct vision. Using the total magnification and the magnification of the eyepiece, we determine the objective lens's role in the microscope, promoting a detailed and clear view of minute specimens.