Given data:
- Objective focal length (f_o) = 5 mm
- Magnification (M) = 400
- Tube length (L_t) = 20 cm

Formula:
The magnifying power (MP) of a compound microscope is given by the product of the magnification of the objective lens (M_o) and the magnification of the eyepiece (M_e).

MP = M_o × M_e

Calculating objective magnification:
Given that MP = 400 and M_o = 400, we can calculate M_e as follows:

400 = 400 × M_e
M_e = 400/400
M_e = 1

Calculating tube length:
The total magnification of a compound microscope is given by the product of the magnification of the objective lens and the magnification of the eyepiece. It is also equal to the ratio of the tube length to the focal length of the objective lens.

MP = L_t/f_o

400 = L_t/5
L_t = 400 × 5
L_t = 2000 mm
L_t = 20 cm

Calculating focal length of the eyepiece:
The focal length of the eyepiece (f_e) can be calculated using the formula:

MP = f_o/f_e

400 = 5/f_e
f_e = 5/400
f_e = 0.0125 mm

Therefore, the focal length of the eyepiece is 0.0125 mm.

Explanation:
- The magnifying power of a microscope is the ability of the microscope to enlarge the image of an object.
- It is given by the product of the magnification of the objective lens and the magnification of the eyepiece.
- In this case, the magnifying power is given as 400, and the magnification of the objective lens is also 400.
- By substituting these values into the formula, we can calculate the magnification of the eyepiece, which is 1.
- The tube length of the microscope is given as 20 cm, which is equal to 2000 mm.
- The total magnification of the microscope is also equal to the ratio of the tube length to the focal length of the objective lens.
- By rearranging the formula, we can calculate the focal length of the eyepiece, which is found to be 0.0125 mm.
- Therefore, the focal length of the eyepiece in this microscope is 0.0125 mm.