A compound microscope has an objective lens with a focal length of 1.5 cm and an
eye piece of focal length 5 cm. It is focused on an object which is at a distance of
1.8 cm. The length of the microscope for normal adjustment is ?
Good
To find the length of the microscope for normal adjustment, we need to use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance from the lens
- u is the object distance from the lens
Let's calculate the length of the microscope step by step:
Step 1: Calculate the image distance (v) from the objective lens.
Given:
- The focal length of the objective lens (f1) = 1.5 cm
- The distance of the object from the objective lens (u1) = 1.8 cm
Using the lens formula:
1/f1 = 1/v1 - 1/u1
Plugging in the values:
1/1.5 = 1/v1 - 1/1.8
Simplifying the equation:
0.6667 = 1/v1 - 0.5556
Rearranging the equation:
1/v1 = 0.6667 + 0.5556
1/v1 = 1.2222
Taking the reciprocal of both sides:
v1 = 0.818 cm
Step 2: Calculate the final image distance (v2) from the eyepiece.
Given:
- The focal length of the eyepiece (f2) = 5 cm
Using the lens formula:
1/f2 = 1/v2 - 1/u2
Since the eyepiece is assumed to be at its least distance of distinct vision, the image distance (v2) is equal to the least distance of distinct vision (D) which is approximately 25 cm.
Plugging in the values:
1/5 = 1/25 - 1/u2
Simplifying the equation:
0.2 = 1/25 - 1/u2
Rearranging the equation:
1/u2 = 1/25 - 0.2
1/u2 = 0.04 - 0.2
1/u2 = -0.16
Taking the reciprocal of both sides:
u2 = -6.25 cm
Note: The negative sign indicates that the image from the eyepiece is virtual.
Step 3: Calculate the length of the microscope (L).
The length of the microscope (L) is the sum of the distances of the objective lens and the eyepiece.
L = |v1| + |u2| (taking the absolute values)
L = |0.818 cm| + |-6.25 cm|
L = 0.818 cm + 6.25 cm
L = 7.068 cm
Therefore, the length of the microscope for normal adjustment is approximately 7.068 cm.
To find the length of the microscope for normal adjustment, we need to use the formula for the compound microscope:
M = L / f
Where:
M is the magnification of the microscope,
L is the length of the microscope, and
f is the focal length of the objective lens.
In this case, the given focal length of the objective lens is 1.5 cm.
Now, to calculate the magnification of the microscope, we use the formula:
M = (D / F) + 1
Where:
D is the distance between the objective lens and the eyepiece, and
F is the focal length of the eyepiece.
In this case, the given focal length of the eyepiece is 5 cm.
To find D, we use the formula for thin lenses:
1 / f = 1 / dO + 1 / dI
Where:
dO is the distance between the object and the objective lens, and
dI is the distance between the image and the objective lens.
In this case, the given distance between the object and the objective lens is 1.8 cm.
So, substituting the values into the formula, we have:
1 / 1.5 = 1 / 1.8 + 1 / dI
Now, solving for dI:
1 / dI = 1 / 1.5 - 1 / 1.8
Now, calculate dI:
1 / dI = 1.8 - 1.5 / 1.8 * 1.5
Once we have dI, we can calculate D:
D = dI + f
Finally, substitute the values of D, f, and F into the formula for magnification:
M = (D / F) + 1
This will give us the magnification of the microscope. From the magnification, we can find the length of the microscope using the formula:
L = M * f
Now, you can plug in the values and calculate the length of the microscope for normal adjustment.