How Do You Calculate the Focal Lengths of Microscope Lenses?

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In summary, the problem involves a microscope with a tube length of 25.0 cm and magnification of 5.00 x 10^2 times by the objective lens and 10.0 times by the eyepiece. The problem is to find the focal lengths of the two lenses using the equations m= H/h=-q/p and q= p(f) / p-f. The solution involves finding the focal lengths of the two lenses by setting up two equations with the given magnification and tube length.
  • #1
strawberry7
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Homework Statement



A microscope is made in a tube 25.0 cm long. It magnifies 5.00 x 10to the 2 times, 50.0 times by the objective lens and 10.0 times by the eyepiece. What are the focal lengths of the two lenses?


Homework Equations


m= H/h=-q/p
q= p(f) / p-f
H= -h(q/p)

The Attempt at a Solution


GIVEN m= 5.00 * 10 to the 2
REQUIRED f= focal length = ? cm is what i am trying to find
I don't think i have the right equation but i don't know which equation to use.
 
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  • #2
u have got f-ob + f-eye = 25 cm...
Now...f-ob / f--eye = m

now u have two variables and two equations ...just solve it out...i couldn't get the later part of the question actually...
 
  • #3


I would suggest using the equation for magnification (m = H/h) to solve for the unknown focal length. The magnification is given as 5.00 x 10^2, which means the image is 500 times larger than the object. This can be written as m = 500 = H/h.

Next, we can use the equation for magnification in terms of focal length (m = -q/p = f_obj / f_eyepiece) to solve for the focal lengths of the objective and eyepiece lenses. Plugging in the known values, we get:

500 = f_obj / f_eyepiece

We also know that the total magnification is the product of the individual magnifications, so we can also write:

m = 500 = 50 * 10 = (f_obj / 25cm) * (10cm / f_eyepiece)

Solving for f_obj and f_eyepiece, we get f_obj = 125 cm and f_eyepiece = 2.5 cm.

Therefore, the focal lengths of the objective and eyepiece lenses are 125 cm and 2.5 cm, respectively.
 

1. What is lens magnification?

Lens magnification is the ratio of an object's size to its image size when viewed through a lens. It is commonly used to describe how much larger or smaller an object appears when viewed through a lens compared to the naked eye.

2. How is lens magnification calculated?

Lens magnification can be calculated by dividing the image size by the object size. It can also be calculated by dividing the focal length of the lens by the object distance or by multiplying the power of the lens by the object distance.

3. What factors affect lens magnification?

The main factors that affect lens magnification are the focal length of the lens, the distance between the lens and the object, and the power of the lens. Additionally, the size and shape of the lens, as well as the refractive index of the lens material, can also affect magnification.

4. How does lens magnification impact image quality?

Lens magnification can impact image quality by altering the size and sharpness of the image. A higher magnification can result in a larger and potentially more detailed image, while a lower magnification may produce a smaller but clearer image. However, other factors such as lens quality and lighting also play a significant role in overall image quality.

5. Is there a limit to lens magnification?

Yes, there is a limit to lens magnification. This limit is determined by the physical properties of the lens and its ability to accurately focus light. Generally, the maximum practical magnification for a lens is around 50 times its diameter in millimeters. Beyond this, the image quality may decrease significantly due to factors such as distortion and aberrations.

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