In a microscope of the type shown in the figure, the focal length of the objecti

Question

In a microscope of the type shown in the figure, the focal length of the objective is 5.12 cm, and that of the eyepiece is 9.72 cm. The distance between the lenses is 26.7 cm. (a) What is the tube length s? (b) If image I in the figure is to be just inside focal point F'_1, how far from the objective should the object be? What then are (c) the lateral magnification m of the objective, (d) the angular magnification m_theta of the eyepiece, and (e) the overall magnification M of the microscope? A) Number units B) Number units C) Number units D) Number units E) Number units

Explanation / Answer

(A)

length of the tube is,

s = l - fob -fey =26.7 - 5.12 - 9.72= 11.8 cm

(B)

the lens equation:

(1 / p) + (1 / q) = (1 / fob)

the image distance is,

q = fob + s = 5.12+11.8= 16.9 cm

then the object distance:

p = (q)(fob) / q -fob

= 16.9*5.12/16.9-5.12,

= 7.34 cm

(C)

the magnification is,

m = - (q / p) = - 16.9/7.34 = -2.30

(D)

the angular magnification is,

mq = 25 cm / fey =26.7/9.72= 2.746

(E)

the overall magnification:

M = (m)(mq) = -2. 30*2.746= -6.31

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