Question

A student microscope has an objective lens that is labeled with a magnification of 10×. Assume a length of L = 120 mm. What focal length eyepiece lens is needed to give an overall magnification of 150x

Answer 1

f_eyepiece = 8.57 mm/x

Step-by-step explanation:

To find the focal length of the eyepiece lens needed to achieve an overall magnification of 150x with a microscope, you can use the formula for the magnification of a compound microscope:

Total Magnification (M_total) = Magnification of the Objective (M_objective) * Magnification of the Eyepiece (M_eyepiece)

The magnification of the objective is given as 10x (M_objective = 10), and you want an overall magnification of 150x (M_total = 150x). Therefore:

M_eyepiece = M_total / M_objective

M_eyepiece = 150x / 10

M_eyepiece = 15x

Now, you can use the formula for the magnification of a simple microscope (single lens) to find the focal length of the eyepiece (f_eyepiece):

M_eyepiece = 1 + (L / f_eyepiece)

Rearrange the formula to solve for the focal length of the eyepiece:

1 + (L / f_eyepiece) = M_eyepiece

(L / f_eyepiece) = M_eyepiece - 1

1 / f_eyepiece = (M_eyepiece - 1) / L

f_eyepiece = L / (M_eyepiece - 1)

Now, plug in the values:

f_eyepiece = 120 mm / (15x - 1)

f_eyepiece = 120 mm / 14x

f_eyepiece = 8.57 mm/x

So, to achieve an overall magnification of 150x, you would need an eyepiece lens with a focal length of approximately 8.57 mm/x.