Final answer:
To calculate the distance between the lenses for a relaxed eye view and the total magnification of a microscope, one must use the thin lens equation for the objective lens and apply magnification formulas for both the objective lens and the eyepiece. For a relaxed eye, the image distance equals the eyepiece focal length. Total magnification is the product of the magnifications from both lenses.
Step-by-step explanation:
The question pertains to calculating the distance between the lenses of a compound microscope adjusted for a relaxed eye and the total magnification of the system when an object is placed at a known distance from the objective lens. To find the answers, we need to use the thin lens equation and the magnification formulas for both the objective lens and the eyepiece.
Calculating the Distance Between the Lenses
(a) For the relaxed eye, the image created by the objective should be at the focal point of the eyepiece. This means the distance between the image produced by the objective lens and the eyepiece should be equal to the focal length of the eyepiece. Using the thin lens equation (1/f = 1/do + 1/di) where f is the focal length, do is the object distance, and di is the image distance, we can calculate the image distance for the objective lens. Once we have this distance, we can add the focal length of the eyepiece to find the total distance between the lenses.
Calculating Total Magnification
(b) The total magnification of a compound microscope is the product of the magnifications of the objective lens and the eyepiece. The magnification of a lens is given by the formula M = -di/do, where M is magnification, di is the image distance, and do is the object distance. After calculating the magnification caused by the objective lens using the previously found image distance, we multiply it by the magnifying power of the eyepiece to get the total magnification.
If any of the needed values, such as the objective lens focal length, are missing in the question, it's impossible to provide an accurate answer without them. In such cases, it is recommended that the student double-checks the components of the problem to ensure all necessary information is included.