The distance between the lenses of a microscope is 18 cm. The focal length of the eyepiece is 1.8 cm. If the microscope is to produce an angular magnification of -260 when used by a person with a normal near point (20 cm from the eye), what must the focal length of the objective be?
Neill
He gave us this in lecture:
L = 0.18m
Fe = 0.018m
M = -260
N = 0.2m
Fo = ?
M = (-N/Fe)(L-Fe/Fo)
Subbed in and I ended up with 6.92x10^-3 m
To determine the focal length of the objective lens, we will use the formula for angular magnification:
Magnification = -do/di
where:
- Magnification is the angular magnification (-260 in this case)
- do is the distance between the object and the objective lens (which we need to find)
- di is the distance between the image and the eyepiece lens (which is the near point distance, 20 cm)
We also know that the distance between the lenses of the microscope (d) is 18 cm, and the focal length of the eyepiece lens (fe) is 1.8 cm.
To find do, we rearrange the formula and solve for do:
Magnification = -do / di
-do = Magnification * di
-do = -260 * 20 cm
do = 5200 cm
Now that we have the value for do, we can calculate the focal length of the objective lens (fo) using the lens formula:
1/f = 1/do + 1/di
Substituting the known values,
1/fo = 1/do + 1/di
1/fo = 1/5200 cm + 1/20 cm
1/fo = (1/5200 + 260/5200) cm
1/fo = (261/5200) cm
To find fo, we take the reciprocal of both sides of the equation:
fo = 5200/261 cm
Therefore, the focal length of the objective lens should be approximately 19.92 cm.