Resolution of a Microscope. The formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. (a) What is the angular magnification of the microscope?

Verified step by step guidance

1. Determine the magnification of the objective lens using the formula \( M_{obj} = \frac{-v}{u} \), where \( v \) is the image distance and \( u \) is the object distance. Since the image is 160 mm from the second focal point and the focal length of the objective is 5.00 mm, calculate \( u \) using \( u = v - f \).
2. Calculate the magnification of the eyepiece using the formula \( M_{eye} = \frac{25}{f_{eye}} \), where \( f_{eye} \) is the focal length of the eyepiece and 25 cm (250 mm) is the near point of the average human eye, which is the distance at which the eye can comfortably see objects in focus.
3. Find the total angular magnification of the microscope by multiplying the magnifications of the objective and the eyepiece together: \( M_{total} = M_{obj} \times M_{eye} \).
4. Substitute the values obtained from steps 1 and 2 into the formula in step 3 to calculate the total angular magnification.
5. Interpret the result: A higher magnification value indicates a greater ability of the microscope to enlarge small details, making them visible to the human eye.

Key Concepts

Focal Length

Focal length is the distance from the lens to the point where parallel rays of light converge or appear to diverge. In microscopes, the focal lengths of the objective and eyepiece lenses are crucial for determining how the lenses will magnify the image. A shorter focal length typically results in greater magnification, which is essential for resolving fine details in microscopic images.

Angular Magnification

Angular magnification is a measure of how much larger an object appears when viewed through a microscope compared to the naked eye. It is calculated as the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the same position. This concept is vital for understanding how effectively a microscope can enhance the visibility of small objects.

Compound Microscope

A compound microscope uses two or more lenses to achieve higher magnification and resolution. The objective lens creates a magnified image of the specimen, which is then further magnified by the eyepiece. Understanding the arrangement and function of these lenses is essential for calculating the overall magnification and resolving power of the microscope.