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Solved: Angular Magnification. In deriving Eq. (34.22) for
Chapter 34, Problem 108P(choose chapter or problem)
Angular Magnification. In deriving Eq. (34.22) for the angular magnification of a magnifier, we assumed that the object is placed at the focal point of the magnifier so that the virtual image is formed at infinity. Suppose instead that the object is placed so that the virtual image appears at an average viewer's near point of , the closest point at which the viewer can bring an object into focus. (a) Where should the object be placed to achieve this? Give your answer in terms of the magnifier focal length
(b) What angle
will an object of height
subtend at the position found in part (a)? (c) Find the angular magnification
with the object at the position found in part (a). The angle
is the same as in Fig.
, since it refers to viewing the object without the magnifier. (d) For a convex lens with
, what is the value of
with the object at the position found in part (a)? How many times greater is
in this case than in the case where the image is formed at infinity? (e) In the description of a compound microscope in Section
, it is stated that in a properly designed instrument, the real image formed by the objective lies just inside the first focal point \(f_{1}^{1}\) of the eyepiece. What advantages are gained by having the image formed by the objective be just inside \(f_{1}^{1}\), as opposed to precisely at \(f_{1}^{1}\) ? What happens if the image formed by the objective is just outside \(f_{1}^{1}\) ?
Equation transcription:
Text transcription:
f{1}^{1}
Questions & Answers
QUESTION:
Angular Magnification. In deriving Eq. (34.22) for the angular magnification of a magnifier, we assumed that the object is placed at the focal point of the magnifier so that the virtual image is formed at infinity. Suppose instead that the object is placed so that the virtual image appears at an average viewer's near point of , the closest point at which the viewer can bring an object into focus. (a) Where should the object be placed to achieve this? Give your answer in terms of the magnifier focal length
(b) What angle
will an object of height
subtend at the position found in part (a)? (c) Find the angular magnification
with the object at the position found in part (a). The angle
is the same as in Fig.
, since it refers to viewing the object without the magnifier. (d) For a convex lens with
, what is the value of
with the object at the position found in part (a)? How many times greater is
in this case than in the case where the image is formed at infinity? (e) In the description of a compound microscope in Section
, it is stated that in a properly designed instrument, the real image formed by the objective lies just inside the first focal point \(f_{1}^{1}\) of the eyepiece. What advantages are gained by having the image formed by the objective be just inside \(f_{1}^{1}\), as opposed to precisely at \(f_{1}^{1}\) ? What happens if the image formed by the objective is just outside \(f_{1}^{1}\) ?
Equation transcription:
Text transcription:
f{1}^{1}
ANSWER:Solution 108P
Step 1
