When the image is formed at infinity, a compound microscope has a magnifying power of 100 . The focal length of the objective is 0.5 cm and the tube length is 6.5 cm . Calculate the focal length of the eyepiece.

Step-by-step solution

For a compound microscope with the final image formed at infinity, the magnifying power is given by: M = |m_o| m_e = ( v_o |u_o| ) ( D f_e ) Using the lens formula for the objective lens, 1 v_o - 1 u_o = 1 f_o : v_o |u_o| = v_o f_o - 1 The tube length L of the microscope when the final image is at infinity is the distance between the objective and the eyepiece, which is given by: L = v_o + f_e v_o = L - f_e Substituting v_o into the magnification formula: M = ( L - f_e f_o - 1 ) ( D f_e ) Given values are: M = 100