Lens formula shows the relationship between object distance u, image distance v and focal length f. This formula is suitable for both convex and concave lenses. lens Formula is 1/u + 1/v = 1/f .
Lens Formula, Derivation, Magnification, Power of Lenses
Lens Formula
Lens formula shows the relationship between object distance, image distance and focal length. This formula is suitable for both convex and concave lenses. lens Formula is 1/u + 1/v = 1/f .
The Lens formula can be used to calculate the distance between the image and the lens.
1/u + 1/v = 1/f.
Where
v = Distance of the image from the lens.
u = Distance of an object from the lens.
f = Focal length of given lens.
The lens formula applies to all situations. If the equation results in negative image distance, then the image is virtual. If the equation shows a negative focal length then the lens is a diverging lens.
A lens is a transparent substance that causes refraction. A lens can focus light rays at a point or disperse light rays.
Lenses that disperse light rays are called diverging lenses and lenses that focus light rays at a single point are called converging lenses.
Lenses Definition
A uniform transparent medium bounded by two curved surfaces or by a curved surface and a flat surface. It is called lens.
Curved surfaces can be spherical, cylindrical and parabolic. But most of the curved surfaces are spherical.
Then the transparent medium falling from the two spherical surfaces is called a lens.
lens type
There are two types of lenses.
1. convex lens
2. concave lens
1. Convex Lens
Those lenses which are thick in the middle and thin at the edges are called convex lenses. Convex lens converges light rays at a point, due to which it is also called converging lens. Convex lenses are used to correct farsightedness.
2. Concave Lens
Those lenses which are thinner in the middle and thicker at the edges are called concave lenses. Concave lens diverges the light rays due to which it is called diverging lens. Concave lens is used for the correction of myopia.
Types of Convex Lens
Convex lens is divided into three parts.
1. Biconvex or double convex lens
2. Plano convex lens
3. Positive Meniscus
1. Bi-convex or bi-convex lens – The lens whose both surfaces are convex. So this type of lens is called biconvex or double convex lens.
2. Plano convex lens - A lens whose one surface is plane and the other surface is convex, then this type of lens is called a plano-convex lens. The definition is clear from the name itself.
3. Positive Meniscus – The lens whose one surface is concave and the other surface is convex. Or the lens whose one surface is depressed and the other surface is convex, then this type of lens is called a concave lens. These surfaces have different radii of curvature.
Type of concave lens
Concave lens is also divided into three parts.
1. Biconcave or bi-concave lens
2. Plano-concave lens
3. Negative Meniscus
1. Bi-concave or bi-concave lens – The lens whose both sides are concave. Or both the surfaces are concave. So this type of lens is called biconcave or bi-concave lens.
2. Plano-concave lens - A lens whose one surface is plane and the other surface is concave, then this type of lens is called a plano-concave lens.
3. Negative Meniscus – The lens whose one surface is convex and the other surface is concave. Or whose one surface is convex and the other surface is depressed, then this type of lens is called a concave lens. These surfaces have different radii of curvature.
Diverging and Converging lens
Convex lens collects the rays of light at a point, due to which convex lens is called converging lens.
And on the contrary, concave lens spreads the rays of light more, due to which concave lens is called diverging lens.
Lenses Definition
Optical center – If the incident ray and the emergent ray of the lens are parallel to each other, then the point at which the refracted ray intersects the principal axis of the lens is called the optical center of the lens.
First focus – The point located on the principal axis of the lens from where the light rays after refraction become parallel to the principal axis is called the first focus of the lens, here is a convex lens.
Derivation of Lens Formula
when an object PQ is held perpendicular to the principal axis at a distance beyond the focal length of the lens then a real, inverted and magnified image P'Q' is formed.
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| Lens formula Derivation |
`\frac{P'Q'}{PQ} = \frac{OQ'}{OQ}`
`\frac{P'Q'}{PQ} = \frac{v}{- u}` ...(eq.1)
In triangle OMF and P'Q'F
`\frac{P'Q'}{OM} = \frac{FQ'}{OF}`
`\frac{P'Q'}{OM} = \frac{OQ' - OF}{OF}`
`\frac{P'Q'}{PQ} = \frac{v-f}{f}` ....(eq.2)
by equation 1 and 2
`\frac{v}{- u} = \frac{v-f}{f}`
`v f = - u (v - f)`
`v f = - u v + uf`
devide by uvf
`\frac{v f}{uvf} = - \frac{u v}{uvf} + \frac{uf}{uvf}`
`\frac{1}{u} = - \frac{1}{f} + \frac{1}{v}`
`\frac{1}{f} = \frac{1}{v} - \frac{1}{u}`
Where
u is object distance from lens,
v is image distance from lens and
f is focal length.
Power of a Lens Formula
The capacity of bending the rays by a lens is known as the power of the lens. In other words we can say more is the ability to bend the light rays greater is the power of the lens. Power of the lens can be defined as under :
Power of lens can be defined as the derivation produced by the lens in the rays coming parallel to principal axis at unit distance from the principal axis.
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| Power of a Lens Formula |
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