Question

A magnifying glass is a single convex lens with a focal length of f = +9.50 cm. (Assume the person using the magnifying glass has a near point of 25 cm and the magnifying glass is directly in front of the person's eyes.)

(a) What is the angular magnification when this lens forms a (virtual) image at ???


How far from the object should the lens be held?


(b) What is the angular magnification when this lens forms a (virtual) image at the person's near point?


How far from the object should the lens be held in this case?

Answer 1

given that, f = 9.5 cm

(a) When the image is at infinite di = ?

angaular magnification given as

M = (1/f - 1/di) N

                        = (1/f - 1/?) N

= ( 1/f -0)N = N/f

then   M = 25 cm / 9.5 cm = 2.63

To obtain the image is at infinte the object should be at focal point of the lens

then from lens formula  

1/f = 1/do + 1/di

1/f = 1/do + 1/?

thus the object distance do = f = 9.5 cm

(b) When the image is at di = - N = -25cm

       then the magnification M = (1/f - 1/di) N

                                              = ( 1/f - 1/-N) N

                                              = (N/f )+ 1

                                              = (25 / 9.5) + 1

                                               = 3.63

Now from lens formula

                 1/f = 1/do + 1/di

    then the object distance is

             do = f di / di -f

                  = (9.5)(25) / (25-9.5) = 15.322 cm