Final answer:
The approximate focal length of the objective lens needed for a microscope with a 10x eyepiece to achieve a total magnification of 200x is 8 mm, considering a standard tube length of 160 mm.
Step-by-step explanation:
To determine the approximate focal length of the objective lens that will give a total magnification of 200x when using a microscope with a 10x eyepiece, we use the formula for total magnification in a compound microscope:
Total Magnification = Magnification of Objective Lens × Magnification of Eyepiece
In this case, the total magnification required is 200x, and the magnification of the eyepiece is known to be 10x. Thus:
200x = Magnification of Objective Lens × 10x
To find the magnification of the objective lens:
Magnification of Objective Lens = 200x / 10x = 20x
We also know that the tube length, L, of a standard compound microscope is 160 mm (L is the distance from the objective lens to the eyepiece). Magnification of the objective lens is approximately given by:
Magnification of Objective Lens ≈ L / Focal Length of Objective Lens
Hence, 20x is approximately equal to 160 mm divided by the Focal Length of Objective Lens:
20x ≈ 160 mm / Focal Length of Objective Lens
Focal Length of Objective Lens ≈ 160 mm / 20x
Focal Length of Objective Lens ≈ 8 mm
The approximate focal length of the objective lens needed to achieve a total magnification of 200x with a 10x eyepiece in a microscope with a tube length of 160 mm is 8 mm.