What Eyepiece Focal Length Achieves a 350x Magnification in a Microscope?

[agenttiny200]

Homework Statement

The distance between the objective and eyepiece lenses in a microscope is 21cm . The objective lens has a focal length of 5.5mm. What eyepiece focal length will give the microscope an overall angular magnification of 350?

Homework Equations

M=(25*d)/(f_e*f_o) or
M=(25*d)/(f_e*f_o)+25?

where d=5.5cm, M=350, f₀=21cm, and f_e is unknown

The Attempt at a Solution

The online program says the answer is 2.4cm using the second equation, so I'm wondering why I don't use the first equation that doesn't add +25, and where the +25 came from? It's really bugging me. (I do not mean the first 25 which is being multiplied by d).

 

[RaulTheUCSCSlug]

Is any more information given by the question? Is the eye relaxed or strained? A strained eye has a different equation from a relaxed eye.

 

[agenttiny200]

Nope. Doesn't give any extra information. That's it.

 

[andrevdh]

There are two formula. The microscope can be setup so that the final image forms either at the near point
(25 cm from the eye) or very far away (infinity). The +25 formula is used when the image is formed at the near point (N = 25 cm) and the other one is used if it is formed very far away.

 

[NascentOxygen]

There are two formula. The microscope can be setup so that the final image forms either at the near point
(25 cm from the eye) or very far away (infinity).

Explained here