The focal length of the objective and eye lenses of a microscope are (1.6 ~cm ) and (2.5 ~cm ) respectively. The distance between the two lenses is (21.7 ~cm ). If the final image is formed at infinity. What is the linear magnification?

Step-by-step solution

Here (v_O=L-f_e=21.7 ~cm -2.5 ~cm =+19.2 ~cm ) (+v e ) sign shows that image is real. For a objective lens ( 1 u_O + 1 v_O = 1 f_O ) [using real-virtual sign convention] ( aligned & 1 u_O = 1 f_O - 1 v_O 1 u_O = 1 (+1.6) - 1 (+19.2) & 1 u_O = 19.2-1.6 (1.6)(19.2) or u_O=+1.745 ~cm aligned ) +ve sign shows that object is real. When the image is formed at infinity, the magnification is given by (m= ( v_O u_O ) ( D f_e ) ) where (D ) is the distance of distinct vision. ( m= ( 19.2 ~cm 1.745 ~cm ) ( 25 ~cm 2.5 ~cm )=11