A student is examining an ant with a magnifying glass. The student\'s near point

Question

A student is examining an ant with a magnifying glass. The student's near point is N=19cm from the eye and the magnifying glass has a focal length of f=8.7cm

A) Write an expression for the angular magnification that the student obsrves, M1, when the image distance of the ant di=-89cm

B) Numerically what is this angular magnification, M1?

C) Write an expression for the angular magnification, M2, when the ant is placed exactly at the focal point of the lens.

D) Numerically what is this angular magnification, M2?

Explanation / Answer

ANS :Q(a): The angular magnification is a maximum when the image is at the near point of the eye—that is, when q = -89 cm. The object distance corresponding to this image distance can be calculated from the thin-lens equation:

1 /f = 1 /p + 1 / q

1/p = 1 /f - 1/q

1/p = 1/f + 1/ 89

1 /p = 89 + f / 89.f

p = 89 f / (89 +f) and the expression for angular magnification is :mmax = 1 + ( 89 / f )

Q(B) :mmax = 1 + ( 89 / f )

          from given data f = 8.7 cm

          m = 1 + ( 89 / 8.7 )

          m = 1 + 10.22

         m = 11.22

Q(C) : mmin = - q / f (when the ant is placed exactly at the focal point of the lens.)

      from given data q = - 89 cm

        m = 89 / f

Q(D) : m = 89 / 8.7

             m = 10 .22

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