As a summer intern for a microscope company, you are designing a compound micros

Question

As a summer intern for a microscope company, you are designing a compound microscope for a client that provides you with the following information. They would like to mount the specimen 105 mm from a 82-mm focal length objective. They want to use a 3.00-cm focal length eyepiece and all lab technicians have normal vision with a near point of 25.0 cm.

(a) Determine the barrel length needed for the microscope. Units in cm

(b) Determine the overall magnification for the microscope (include the sign).

Explanation / Answer

(a) Use the expression -

1/s + 1/s' = 1/f

for the objective -

1/0.105 + 1/s' = 1/0.082

=> 1/s' = 12.20 - 9.52 = 2.68

=> s' = 0.373 m

so, m1 = - s'/s = - 0.373/0.105 = - 3.55

Now, for the eyepiec -

s = 0.373 + 0.105 = 0.478 m

s' = ?

f = 0.03 m

so -

1/0.478 + 1/s' = 1/0.03

=> 1/s' = 33.33 - 2.09 = 31.24

=> s' = 0.032 m

Now, angular magnification of eyepiece, m(e) = 25/3 = 8.33

therefore, length of the barrael = 0.373 + 0.032 = 0.405 m = 405 mm

(b) Overall magnification of the microscope, M = m1 x m(e) = -3.55 x 8.33 = - 29.6

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