To examine a particular blood sample in biology lab, a student uses a compound m

Question

To examine a particular blood sample in biology lab, a student uses a compound microscope set to have a magnification of -4500. The objective and eyepiece are both attached to a tube which is 18 cm in length and the eyepiece has a focal length of 2.67 cm. The near point of the person using the microscope is 25.5 and you can assume she can view the image produced with a fully relaxed eye.

What is the focal length of the objective? I got 0.0382 which is not correct.

What is the distance between the blood sample and the objective lens?

Explanation / Answer

Given

compound microscope of

total magnification M = -4500

length of the tube is L = 18 cm

focal length of the eye piece is fe = 2.67 cm

near point of the person N = 25.5 cm

then focal length of the objective lens f0 = ?

and the object distance that is the distance from blood sample to the objective lens f0 = ?

from the magnifications of the compound microscope  

the objective lens magnification is Mo = di/do = L-fe/d0

and eye piece is Me = N/fe

and total magnification is M = Mo*Me

Mo = 18-2.67/d0

Me = 25.5/2.67

so M= ((18-2.67)/do)(25.5/2.67 ) = 4500

solving for d0 , do = 0.0325355 cm

so the objective distance that is the distance between the blood sample and the objective lens is do = 0.0325355 cm

from the general relation of lens  

1/d0 +1/di = 1/f0

1/0.0325355+1/(18-2.67) = 1/f0

f0 = 0.032466 cm

the focal length of the objective lens is f0 = 0.032466 cm

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