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A typical red blood cell subtends an angle of only 1.9x10^-5rad when viewed at a person's near-point distance of 25cm . Suppose a red blood cell is examined with a compound microscope in which the objective and eyepiece are separated by a distance of 12.0cm . Given that the focal length of the eyepiece is 2.7cm , and the focal length of the objective is 0.49cm ,find the magnitude of the angle subtended by the red blood cell when viewed through this microscope.

Explanation / Answer

The angular magnification M = 25/f1 * s'/f2 where s' is the image distance from the objective so -

M = 25/f1*(d - f1)/((d - f1)*f2/(d - f1 -f2))
where -
d= 12.0 cm
f1 = 2.70cm
f2 =0.49cm

So M = 25/2.7* (12.0 - 2.7 ) / ( ( 12.0 - 2.7 )*0.49 / ( 12.0 - 2.7 - 0.49)) = 166.47

Angle subtended is 166.47* 1.9x10^-5 rad = 3.16x10^-3 rad

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