How Do You Calculate Angular Magnification in a Microscope?

[klminch]

Homework Statement

The image formed by a microscope objective with a focal length of 5 mm is 160mm from its second focal point. The eyepiece has a focal length of 26mm.

a.what is the angular magnification of the microscope?

Homework Equations

Mtotal=M_e*m_o

m_o= linear magnification of objective. m_o=-L/f_o, where L is the distance from the first lens to the first image, and f_o is the focal length of the objective.

M_e=25/f_e where M_e= angular magnification of the eyepiece.

The Attempt at a Solution

So M_e=25*10/26= 9.6154, since 25 is referring to the near point in cm, I converted it to mm.

m_o= 160/5= 32
M=32*9.6154=307.69.

However, the correct answer is 317 so I'm about 10 off and I don't know why. I think I may be using the L term incorrectly as I don't really understand what the 160mm value is referring too. Any help would about where I went wrong above would really be appreciated.

Thanks!

 

[anathema]

It looks like you have the right approach, but the issue may be with your conversion of the near point from cm to mm. Instead of converting it to mm, try converting it to meters. This will give you a more accurate value for the angular magnification. Also, make sure you are using the correct values for the focal length of the objective and the distance from the first lens to the first image. The 160mm value is referring to the distance from the second focal point of the objective to the first image formed by the objective. So in your calculation for m_o, you should use a value of 155mm (160mm - 5mm). This should give you a more accurate result.