Optical Instruments — Question 7

Question 7

A compound microscope multiplies transverse and angular magnifications

A microscope objective has fo=0.80 cm and an object at po=0.84 cm. The eyepiece has fe=4.0 cm and is positioned to give parallel final rays. Use reference near-point distance D=25 cm and neglect lens thickness.

1. Find the objective image distance, magnification, and required lens separation.

2. Find total signed angular magnification relative to unaided viewing at D.

Question 7 - Solution

A compound microscope multiplies transverse and angular magnifications

(a) Method and calculation

$$q_o=\frac{0.80(0.84)}{0.84-0.80}=\boxed{16.8\,\mathrm{cm}},\quad m_o=-q_o/p_o=\boxed{-20}.$$$$\boxed{d=q_o+f_e=20.8\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$M_e=D/f_e=25/4=6.25.$$$$\boxed{M=m_oM_e=-20(6.25)=-125}.$$

Physical check

The objective forms an inverted real intermediate image at the front focal plane of the eyepiece; the final viewed image is inverted relative to the original.