Final answer:
To find the separation between the lenses in a compound microscope, one must use the object location, focal lengths of the lenses, and the desired magnification setting, inferring from the normal near point and principles of geometric optics.
Step-by-step explanation:
To find the separation between the two lenses of a compound microscope, we use the formula for the total magnification produced by the microscope when forming a final image at the near point of the eye. The compound microscope consists of two lenses: The objective lens and the eyepiece. The object is placed a little outside the focal length of the objective lens to create a real, inverted and enlarged image of the object. This image then acts as the object for the eyepiece which further magnifies the image and makes it virtual and erect for the viewer to see.
To calculate the separation, we need to consider the intermediate image position (I), which can be found using the lens formula for the objective: 1/Fo = 1/do + 1/I, where Fo is the focal length of the objective lens and do is the distance of the object from the objective lens. Once you have I, you can calculate the total magnification (M) using the magnification of the objective (Mo), which is I/do, and the magnification of the eyepiece (Me), which is 25cm/Fe, where Fe is the focal length of the eyepiece.
In the given problem, the total distance from the object to the user's near point (25cm) is the sum of the separation of the two lenses (L) and the 9cm from the object to the objective. Thus, the image formed by the objective lens is at a distance I from the objective where I = L + 9cm, and this image is located at the person's near point. By applying the lens formula and the magnification formulas, we can solve for L.
The total magnification is not explicitly given in this question, but we can infer from the normal near point (25cm) and the objective and eyepiece focal lengths to find the required separation distance, L, using magnification equations and principles of geometric optics.