Question

The distance between the objective and eyepiece lenses in a microscope is 25cm . The objective lens has a focal length of 4.0mm .

Part A

What eyepiece focal length will give the microscope an overall angular magnification of 200?

*******SHOW ALL WORK PLEASE

Answer 1

The magnitifcation of the objective is

  m_o = L / f_o

Here, distance between objcetive and eyepiece is L and focal lenght of the objective is f_o.

Subsitute the values,

m_o = L / f_o

= 25 cm / (4.00 mm)(10^-1 cm/1 mm)

= 62.5

Magnification of the eyepice is

m_e = 25 cm / f_e

Here, focal length of the yeypiece is f_e.

Now, the overall angular magnification of the microscope is

  m = m_o x m_e

Subsitute the values,

m = m_o x m_e

200 = (62.5) (25 / f_e)

f_e = 7.8125 cm

Rounding off two significant figures, the focal lenght of the eyepiece is 7.8 cm.