The near point of a naked eye is 25 cm, when placed at the near point and viewed

Question

The near point of a naked eye is 25 cm, when placed at the near point and viewed by the naked eye, a tiny object would have an angular size of 5.2 × 10-5 rad, when viewed through a compound microscope, however, it has an angular size of -7.20 x 10-3 rad. (The minus sign indicates that the image produced by the microscope is inverted. The objective of the microscope has a focal ength of 2.5 c and the distance between the objective and the e eie ei 15 ?? . Find the focal length of the eyepiece 007 Xcm

Explanation / Answer

The near point of the object,N = 25 cm
Angular size of the object as viewed by naked eye,? =5.2x10-5 rad
Angular size as observed through a compound microscope,?' =-7.20x10-3 rad
focal length of the objective of the microscope,fo = 2.5cm
Distance between the objective and the eye piece,L = 16 cm

Now the angular magnification is given by

                     M = ?'/?
                          = -7.20x10-3 /5.2x10-5

                           =-138.461
For compound microscopes,
                      M = - (L-fe)N/fofe
               138.461 = (16 - fe) 25 / 2.5fe

                138.461= (400 -25fe)/2.5fe

            346.1525fe = 400 -25fe

      371.1525fe = 400  

                        fe = 400/371.1525

                            = 1.0777cm

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