The lenses used in a compound microscope have powers of + 110 D and + 60 D .
If a total magnification of -150 × is desired, what should be the distance between the two lenses?
To determine the distance between the two lenses in a compound microscope, we need to use the lens formula. The lens formula relates the focal length (f) of a lens to the object distance (u) and the image distance (v):
1/f = 1/v - 1/u
In a compound microscope, the total magnification (M) is the product of the magnifications of the individual lenses:
M = M1 × M2
Where M1 is the magnification of the first lens and M2 is the magnification of the second lens.
In this case, the total magnification M is given as -150×. The magnification of a lens depends on the focal length. The magnification formula for a lens is:
M = -v/u
Given that M = -150×, we can find v/u = 150.
To find the distance between the two lenses, we need to find the value of u, the object distance for the second lens.
We know that the focal length (f) of a lens is related to its power (P) by the formula:
f = 1/P
For the first lens with a power of +110 D, f1 = 1/110 m^(-1).
We can substitute these values into the lens formula for the first lens and solve for v1:
1/f1 = 1/v1 - 1/u
Substituting f1 = 1/110 m^(-1), we can solve for v1.
Next, we can calculate M1, the magnification of the first lens using the formula M = -v/u and substituting the value of v1 we just found.
Now that we have M1, we can find M2. Since M = M1 × M2 and M = -150, we can solve for M2.
Finally, we can calculate the object distance (u) of the second lens using the magnification formula and the value of M2 we just found.
Once we have the value of u, we can calculate the distance between the two lenses by subtracting the object distance (u) of the second lens from the sum of the focal lengths of the two lenses.