object location, focal length, linear & overall magnification

Question

A crude microscope consists of an objective of 1.5 cm focal length & eyepiece of 5 cm focal length. Lenses are placed 18 cm apart. A person uses the microscope to form an image at infinity. Where must the object be placed? What is the linear magnification of the objective? The angular magnification of the eyepiece? The overall magnification?

Answer 1

What we are given:

1. Fo(objective)=1.5cm
2. Fe(eyepiece)=5cm
3. L=18cm
4. D=25cm

1) We need to use the thin-lens equation.1/fo = 1/uo + 1/vo ; looking for uo. We will see that we are missing vo in the equation, so we need to find it. vo=L-fe=18-5cm=13 cm

1/1.5 = 1/uo + 1/13 ----> 0.6667=1/uo + 0.0769 ; 1/uo=0.5898 ; uo=1.70cm

2) Magnification formula: mo=vo/uo = 13/1.70 =7.6

3) Eye piece: Me=D/fe = 25/5= 5

4) M total= mo * Me = 7.6 * 5= 38