Final answer:
The total angular magnification of the microscope is -457.62, indicating that the image seen is inverted. This is calculated by multiplying the magnification of the objective by the angular magnification of the eyepiece.
Step-by-step explanation:
The total angular magnification (M) of a compound microscope is the product of the magnifications of the objective lens and the eyepiece. The magnification (mobj) of the objective is given by the equation mobj = -L/fobj, where L is the tube length (155 mm in this case) and fobj is the focal length of the objective (3.77 mm). The negative sign indicates that the image is inverted relative to the object. The angular magnification (Meye) of the eyepiece is similar to that of a simple magnifying glass and is given by Meye = 1 + (D/feye), where D is the near point distance (25.0 cm). The total magnification is the product M = mobj × Meye.
To calculate the magnifications:
Calculate the magnification of the objective: mobj = -L/fobj = -155 mm/3.77 mm = -41.12 (rounded to two decimal places).
Calculate the angular magnification of the eyepiece: Meye = 1 + (D/feye) = 1 + (250 mm/24.7 mm) = 11.13.
Calculate the total angular magnification: M = mobj × Meye = -41.12 × 11.13 = -457.62.
The image seen through the microscope is inverted due to the negative magnification of the objective lens.