How Do Compound Lenses Improve Image Formation?
A lens is a portion of a transparent refracting medium bound by two spherical surfaces or one spherical surface and the other plane surface.
Lenses are used to focus light so that a person can get a clear picture of the objects.
The Commonly Used Lenses are of Two Types
Convex (Converging lens)
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Concave (Diverging lens)
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There are Certain Uses of Lens In our Life Such as :
We see many people do observe nearby things and find it difficult in observing far objects (myopia) for which they use spectacles or contact lenses that are concave in shape.
Many people can see far objects while they find irt hard in observing nearby objects (hypermetropia) for which they use convex lenses while some people facing astigmatism are recommended to use cylindrical lenses..
Compound Lenses Thin Lenses in Contact
In various optical instruments like microscopes,telescopes, two or more lenses are combined to get the following requirements:
Increase the magnification of the image.
Obtain the erect image of an object.
Reduce aberrations or defects caused by using a single lens.
The position, size and nature of the final image produced by the combination of thin lens can be represented by a ray diagram as shown below:
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In Figure.1, we have used two thin convex lenses placed on the common principal axis.
Let C₁, C₂ be the optical centers of two thin lenses L₁ and L₂.
These lenses are held co-axially with each other in the air.
Suppose, f₁ and f₂ be their respective focal lengths.
Let’s place an object at point O on the principal axis at a distance OC₁ = u.
The Lens L₁ would alone form its image at I’.
Here, C₁I’ = v’.
From the Lens formula, we obtain our first equation:
1/v’ - 1/u = 1/f₁ - (1)
Looking at Figure.1, this I’ would serve as a virtual object for lens L₂.
Thus, image is formed by this virtual object at I.
Where the distance C₂ I = v.
Since these lenses are thin.
Therefore, we can say for lens L₂ i.e.,
u = C₂ I’ ≈ C₁I’ = v’
Now, let’s obtain an equation for lens L₂,
1/v - 1/v’ = 1/f₂…(2)
Adding (1) and (2), we get
1/v’ - 1/u + 1/v - 1/v’ = 1/f₁ + 1/f₂
1/v - 1/u = 1/f₁ + 1/f₂….(3)
Here, eq(3) is similar to the lens formula for the focal length in a combination of two lenses.
Now, if we replace these two lenses by a single focal length F which forms image I at a distance v of object at distance u.
Then,
1/v -1/u =1/F…(4)
Which means,
1/F =1/f₁ + 1/f₂
If we consider taking one lens as a convex lens of focal length f₁ and the other of concave lens with focal length f₂ then,
1/F = 1/f₁ + 1/ -f₂
If we take ‘n’ no of lenses, then effective focal length of the combination will be:
Total magnification of the combination is the product of magnification of individual lenses, given by,
m = m₁ x m₂ x m₃ x ….x mₙ
Afocal Definition
A system that outputs parallel rays with input rays.
The prominent examples for the same are telescopes, beam expanders, etc.
Afocal
Afocal is an optical system that has an infinite focus.
Afocal projection is a method of photography in which a lens attached with a camera is mounted over the eyepiece of another image forming an optical system such as a telescope or microscope.
Here, the lens of a camera acts as a human eye.
Afocal System
Afcoal system is an optical system that produces no net convergence or divergence of the beam.
Let us discuss the combination of thin lenses that produces afocal systems.
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Fig.2 : Thin lenses in contact
This system is formed by the combination of two focal systems.
In Fig.2, the rear focal point of lens F₁’ is coincident with the focal length of the second lens F₂ .
Since object and image rays are parallel to the axis.
Therefore,magnification will be constant given by,
h₀/ - f₁ = hᵢ / f₂
Magnification (m) = height of image /height of object = hᵢ / h₀
Here, the system magnification is negative.
The sum of the individual focal lengths is equivalent to:
Such a configuration forms the basis for a Keplerian telescope.
Therefore, imaging equations for focal systems do not apply to afocal systems as there are no focal points. However, focal systems can form images.
FAQs on Compound Lenses: Meaning, Working, and Applications
1. What is a compound lens and why is it used?
A compound lens is an optical system made of two or more simple lenses aligned along a common axis. It is used instead of a single lens to minimise optical distortions, known as aberrations. By combining different types of lenses (e.g., convex and concave), a compound lens can correct issues like chromatic aberration (colour fringing) and spherical aberration (blurring), resulting in a much clearer and more precise image.
2. How do you calculate the equivalent focal length for two thin lenses in contact?
For two thin lenses with individual focal lengths f₁ and f₂, placed in direct contact, you can calculate the equivalent focal length (F) using the formula: 1/F = 1/f₁ + 1/f₂. The total power (P) of this combination is simply the algebraic sum of their individual powers, so P = P₁ + P₂.
3. What are some common real-world examples of compound lenses?
Compound lenses are essential in most modern optical instruments. Key examples include:
- Camera Lenses: A typical camera lens contains multiple lens elements to produce sharp, high-quality photographs without distortion.
- Microscopes: Both the eyepiece and the objective lens in a compound microscope are themselves compound lenses, designed to achieve high magnification.
- Telescopes: Refracting telescopes use a compound objective lens to gather light and correct for chromatic aberration.
- Eyeglasses: High-power or specialised eyeglasses, like bifocals or progressive lenses, can be considered a form of compound lens system.
4. What is chromatic aberration, and how do compound lenses correct it?
Chromatic aberration is an optical defect where a single lens fails to focus all colours of light at the same point, causing a blurry image with rainbow-like edges. This occurs because the refractive index of glass varies with the wavelength of light. A common solution is an achromatic doublet, a compound lens made of a convex crown glass lens and a concave flint glass lens cemented together. This combination is designed to bring two primary colours (like red and blue) to a common focus, significantly reducing the aberration.
5. How does the formula for a compound lens change if the lenses are separated by a distance?
When two thin lenses with focal lengths f₁ and f₂ are separated by a distance 'd', their combined focusing power changes. The formula for the new equivalent focal length (F) is no longer a simple sum and is given by: 1/F = 1/f₁ + 1/f₂ - d/(f₁f₂). This principle is fundamental in designing complex optical systems like zoom lenses, where the distance between lens elements is intentionally varied.
6. What is the key difference between an achromatic and an apochromatic lens combination?
The primary difference is the degree of colour correction they offer. An achromatic lens is designed to bring two different wavelengths (e.g., red and blue) to the same focal point, which greatly reduces colour fringing. An apochromatic lens provides a higher level of correction by bringing three different wavelengths (e.g., red, green, and blue) to a single focal point, resulting in an exceptionally sharp image with almost no chromatic aberration.
7. Can a combination of a convex and a concave lens act as a converging system?
Yes, it is possible. A system with both a convex and a concave lens will act as a converging system if its net power is positive. This occurs when the power of the convex lens is greater than the magnitude of the power of the concave lens (P_convex > |P_concave|). In this scenario, the combination will have a positive equivalent focal length and will be able to form a real image, similar to a single convex lens.
