To examine a particular blood sample in biology lab, a student uses a compound m
ID: 306877 • Letter: T
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