Final answer:
The question involves calculating the distance between the objective and eyepiece lenses in a microscope using the lens formula and the condition of minimum eyestrain for a given near point.
Step-by-step explanation:
The question is about calculating the distance between the objective and the eyepiece of a microscope when an object is placed at a specific point from the objective, given the focal lengths of both the objective and eyepiece lenses and the condition of minimum eyestrain for a person with a particular near point.
To find the distance between the objective and the eyepiece, we use two principles: the lens formula to find the image position from the objective lens and the condition of minimum eyestrain, which implies the final image must be at the observer's near point. The lens formula states that 1/f = 1/di + 1/do, where f is the focal length, di is the image distance from the lens, and do is the object distance from the lens.
First, we apply the lens formula for the objective lens of focal length 2.90 mm with the object 3.00 mm away. Since the object is very close to the focal length, a real, inverted image is formed at a distance di from the objective lens on the opposite side. This real image will act as an object for the eyepiece lens. If we adjust the microscope for minimum eyestrain, the eyepiece should form a virtual image at the person's near point, which is 25 cm away from the eyepiece lens. Using the lens formula again for the eyepiece, we find where the real image must be relative to it, which will give us the desired distance between the objective and the eyepiece.