Final answer:
The magnification of the eyepiece is 4x. The possible total magnifications are 400x and 1600x.
Step-by-step explanation:
(a) To find the magnification of the eyepiece, we divide the overall magnification by the magnification of the objective lens. In this case, the overall magnification is 800 and the magnification of the objective is 200. So, the magnification of the eyepiece is 800/200 = 4x.
(b) To find the other total magnifications, we multiply the magnification of the eyepiece by the magnification of each objective lens. The possible total magnifications are:
- 100x eyepiece: 100 x 4 = 400x
- 400x eyepiece: 400 x 4 = 1600x
The magnification of a microscope is the product of the magnification powers of the objective lens and the eyepiece. Given that a microscope has an overall magnification of 800x and an objective lens that magnifies by 200x, we can calculate the magnification of the eyepiece with the formula:
Total Magnification = Objective Magnification × Eyepiece Magnification
Substituting the known values, we have:
800 = 200 × Eyepiece Magnification
Dividing both sides by the magnification of the objective lens (200x), we find the magnification of the eyepiece:
Eyepiece Magnification = 800 / 200 = 4x
For the second part, if other objectives have magnifications of 100x and 400x, the possible total magnifications achieved with the same eyepiece would be:
100x (objective) × 4x (eyepiece) = 400x
400x (objective) × 4x (eyepiece) = 1600x
Therefore, the magnification of the eyepiece is 4x, and the other total magnifications possible are 400x and 1600x.