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In the world of microscopy, the objective lens is crucial as it is responsible for gathering light from the specimen and creating an enlarged image. This lens is positioned close to the object being examined. The main task of the objective lens is to magnify the specimen, and this is done by focusing on creating real, inverted images. - **Magnification:** The magnification power of the objective lens is determined by the ratio of the image distance (\( d_i \)) to its focal length (\( f_o \)). Therefore, in practical terms, the formula for magnification (\( M_o \)) is \( M_o = rac{d_i}{f_o} \).
- **High Magnification:** In our example, with a focal length of 5.00 mm and an image distance of 160 mm, the objective lens provides a significant magnification factor of 32. This high power magnification allows detailed observation of small objects, which is especially useful in biological and material science research.

Angular magnification is a critical measure in microscopes, as it represents how much larger the viewed angle through the microscope is compared to viewing with the naked eye at a normal distance. Essentially, angular magnification is about how big the image appears to our eyes. - **Formula:** The angular magnification of the microscope is calculated by multiplying the magnification of the objective lens (\( M_o \)) by that of the eyepiece lens (\( M_e \)). So the total angular magnification (\( M_t \)) is given by \( M_t = M_o imes M_e \).
- **Application:** In our scenario, the total angular magnification comes out to be 308.8, meaning the image appears over 300 times larger than what the naked eye would see under normal conditions. This extensive enlargement can reveal details that are invisible without such magnification.

The eyepiece of a microscope plays a substantial role in magnifying the image initially formed by the objective lens. The focal length of the eyepiece lens determines its magnification power and influences the comfort and ease with which the image can be viewed. - **Focal Length and Magnification:** The eyepiece focal length (\( f_e \)) is inversely related to its magnification power. Shorter focal lengths result in higher magnification. For example, an eyepiece with a focal length of 26.0 mm helps further enlarge the image due to its angular magnification (\( M_e \)), which is calculated as \( M_e = rac{25 ext{ cm}}{f_e} \).
- **Practical Importance:** In the exercise, the eyepiece contributing a magnification factor of approximately 9.62 enhances viewing significantly. This fine adjustment by the eyepiece ensures that the final image is not only magnified but also clear and comfortable to view.