Finding the focal length of the lense

In summary, when using a spectacle magnifier, the maximum magnification the lens can produce is 5x. The focal length of the lens is 6.25cm.
  • #1
Aladin
77
0

Homework Statement


A magnifying glass gives a five times enlarged image at a distance of 25 cm from the lense.Find the focal length of the lense
d=25cm
M=5
f=?

Homework Equations


f = d/M


The Attempt at a Solution


f = 25/5
f = 5 cm

But this solution is not correct please help me and explain also.
thanks
 
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  • #2
hrm interesting.
When a spectacle magnifier produces an image 25cm in front of the lens you need to use the formula for maximum magnification. The fact that the distance to the cornea has not been specified also suggests this. In other words 5x is the maximum magnification that this lens can produce, should the lens be held say 10cm from the cornea the magnification would be less. This is a special case of angular magnification where the magnification is at a maximum due to the cornea being virtually in contact with the lens and the image being produced at the reference seeing distance (25cm)
Anyways here's the formula...M(max)=1+F/4
which when rearranged gives... (M-1)*4=F
substitute into formula...(5-1)*4=F
therefore F=+16.00D
to find focal length we take the reciprocal of F...1/F = 1/16 = 0.0625m or 6.25cm

hope this is useful
 
Last edited:
  • #3
M(max)=1+F/4

what is 4 in this formula?
 
  • #4
Aladin said:
M(max)=1+F/4

what is 4 in this formula?

This formula as i stated previously is a special case of angular magnification when the magnification is at a maximum. It is derived from;
M = qL / 1-dL', where q is the least distance of distinct vision, L and L' are the vergences of light entering and leaving the lens respectively and d is the distance to the cornea.
The proof for maximum magnification is as follows;
Angular mag will be at a maximum when the image is formed at least distance of distinct vision ( l'=-0.25m) and the eye is placed close to the lens so that d=0, substituting into the equation with d=0, L = L' - F = -4 - F,
where L'=1/l' =1/-0.25 = -4D then,
M = qL / 1-dL'
M = (-0.25)(-4-F) / 1-(0xL')
M = 1 + 0.25F
M(max) = 1 + F/4

Hope this clarifies things :)
 

What is the focal length of a lens?

The focal length of a lens is the distance between the lens and the point where all of the light rays converge to a single point. It is usually measured in millimeters (mm) and is a key factor in determining the magnification and field of view of a lens.

How do you find the focal length of a lens?

To find the focal length of a lens, you can use a variety of methods such as measuring the distance between the lens and the image sensor, using a lens equation, or using a lensometer. The specific method will depend on the type of lens and equipment you have available.

What factors affect the focal length of a lens?

The focal length of a lens is primarily affected by the curvature of the lens surface, the thickness of the lens, and the refractive index of the material the lens is made from. Other factors such as the shape and design of the lens can also play a role in determining the focal length.

How does focal length impact image quality?

The focal length of a lens can impact image quality in a few ways. A longer focal length can result in a narrower field of view and a larger magnification, which can be beneficial for capturing distant objects but may also result in a loss of image quality due to distortion and chromatic aberration. A shorter focal length can result in a wider field of view and a smaller magnification, which can be useful for capturing landscapes or group shots but may also result in a loss of sharpness towards the edges of the image.

Can the focal length of a lens be changed?

The focal length of a lens is determined by its physical properties and cannot be changed. However, some lenses have variable focal lengths, such as zoom lenses, which allow the user to adjust the focal length within a certain range. Additionally, some lenses have interchangeable elements, such as teleconverters, which can effectively change the focal length of the lens they are attached to.

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