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The focal length of a lens is crucial to understanding how a microscope magnifies an object. It represents the distance between the lens and the point where parallel rays of light converge to a focus. Short focal lengths mean stronger magnifying power because they converge light more quickly. For example, in the given exercise, the lenses have focal lengths of 16 mm, 4 mm, and 1.9 mm. A shorter focal length like 1.9 mm provides higher magnification because the light focuses more rapidly, making objects appear larger. This is similar to how a zoom lens on a camera works.
To calculate how much an objective lens magnifies, we use the formula: \( m_o = \frac{l}{f_o} - 1 \) where \(l\) is the image distance and \(f_o\) is the focal length. A smaller \(f_o\) results in a higher value for \(m_o\), indicating greater magnification capacity.

Angular magnification refers to how much larger an object appears when viewed through a microscope compared to the naked eye. It is determined by multiplying the magnifications of both the objective lens and the eyepiece.
The exercise provided different eyepieces with angular magnifications of \(5 \times\) and \(10 \times\). This means that the eyepiece alone makes an object look 5 to 10 times bigger than it appears without magnification. For instance, if an eyepiece has an angular magnification of \(10 \times\) and it combines with an objective lens that magnifies \(62.1\), the total angular magnification becomes \(621\).
Angular magnification is a product of the optics involved and shows how significantly an image can be expanded to appear larger through a microscope.

The optical objectives of a microscope are key components that determine how much detail can be observed in a specimen. An objective lens captures light from the sample and creates a real image of the specimen at a certain magnification.
In the case of the exercise, various lenses with focal lengths of 16 mm, 4 mm, and 1.9 mm represent distinct optical objectives. Each creates a different image size before the eyepiece further magnifies it. The shorter focal length objectives provide higher magnification and better detail, essential for examining tiny structures. For instance, the smallest objective (with 1.9 mm focal length) provides the highest magnification due to its smaller focal distance, allowing it to form a larger initial image.
The choice of objective is crucial in microscopy as it directly affects resolution and brightness of the image.