How Far Should the Object Be Placed in a Microscope Setup for 75x Magnification?

[mithil03]

Homework Statement

Suppose we have a microscope made out of two lenses, both with a focal length of
25mm, placed 36.5mm apart. Find how far in front of the first lens should the object be
placed to assure that the image is magnified at least by a factor of 75?

Homework Equations

The magnification for a compound microscope is : Mo x Me = (V/fo - 1) (1+ D/fe) or (-L/f1) (25/f2)

Lens formula: 1/v - 1/u = 1/f

The Attempt at a Solution

Not sure which equation to use as the first one doesn't make use of the distance btw the two lenses. And still not sure how Ill get the position of object from the first lens.

 

[rl.bhat]

Mo x Me = (V/fo - 1) (1+ D/fe) or (-L/f1) (25/f2)

In the above formula V is the image distance. But you want the object distance. SO the formula can be rewritten as

MoxMe = fo/(fo+u)(1 + D/fe)

Now find u.

 

[mithil03]

But I am still not using the value of the distance between the two lenses at all. By the above equation I am getting the answer as -73/3 .

 

[rl.bhat]

According to me

75 = 2.5/(u - 2.5)*(1 + 25/2.5)

Solve it and find u. In this method length of the tube not necessary.

 

[mithil03]

The formula is fo/(fo+u) right ? Here you are taking u-fo in the denominator ...Am i right ?

 

[rl.bhat]

In the relevant equation you have written

1/v - 1/u = 1/f.

When you apply the sign convention, for the real image in convex lens the formula becomes

1/v + 1/u = 1/f. Multiply by u on both the sides. You get

u/v + 1 = u/fo Or

1/mo = u/fo - 1 Or

mo = fo/(u - fo)