Power that a Lens

The strength of a lens is mentioned as p = \<\frac1F\>, where f is the focal length.

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The S.I. Unit of strength of a lens is \. This is likewise known as diopter.

The focal length (f) that a converging lens is considered positive and that that a diverging lens is thought about negative. Thus, the strength of a converging lens is positive and that that the diverging lens is negative.

Lens Formula in terms of Power

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Fig.1 shows two lenses \ and \ inserted in contact. The focal distance lengths the the lenses space \ and also \ respectively. Let ns be the point where the optical centers that the lenses coincide (lenses being thin).

Suppose, a allude object is placed at a allude O beyond the emphasis of lens \ such the OP = u (object distance) top top the common principal axis (coaxially). The very first lens \ alone forms an image at \ where P1 = \ (image distance). This point I1 works as the online object for the 2nd lens \ and also the last image is formed at I, in ~ a street PI = v. The ray diagram(Fig.1) formed by the combination of 2 convex lenses has the complying with attributes:

u = Object-distance because that the an initial lens

v = final image-distance for the second lens

\ = image-distance because that the first image I1 for the first lens. As the lenses room pretended to be thin, \ is also the object-distance for the second lens.

The lens formula for the image \ formed by lens \ will certainly be

\<\frac1v_1\> - \<\frac1u\> = \<\frac1F\> ….(1)

The equation because that the image development for the second lens \

\<\frac1v\> - \<\frac1v_1\> = \<\frac1f_2\>….(2)

Adding eq(1) and also (2):

\<\frac1v_1\> -\<\frac1u\> + \<\frac1v\> - \<\frac1v_1\> = \<\frac1F_1\> + \<\frac1f_2\>

\<\frac1v\> - \<\frac1u\> = \<\frac1F_1\> + \<\frac1f_2\>….(3)

The Focal length of the merged Lens is given by

If the mix is replaced by a single lens the focal length F such that it develops the image of O at the place I,

\<\frac1v\> - \<\frac1u\> = \<\frac1F\>……(4)

This type of lens is referred to as the equivalent lens for the combination.

Combining (3) and also (4),

\<\frac1F\> = \<\frac1f_1\> + \<\frac1f_2\>……(5)

Here, F is the focal length of the identical lens for the combination. As the power of a lens is p = 1/F, eq (5) instantly gives

The strength of any number of lenses in contact is same to the algebraic sum of the power of two individual lenses.

This is true for any situation including two thin lenses in contact.

How to find the strength of the Lens making use of the focal Length?

The power of a lens is measured as the reciprocal of the focal size of the lens.

Relation v focal length: A lens of much less focal size produces an ext converging or diverging and also is said to have more power.


Here, v = refractive table of contents of the material

\ = Radius the curvature the the first surface of the lens

\ = Radius the curvature that the 2nd surface that the lens

For a converging lens, strength is taken as positive and for a diverging lens, strength is taken as negative.

Power that Lens and its Unit

The S.I. Unit of strength is dioptre (D).

When f = 1 meter, p = \<\frac1F\> = 1/ 1 = 1 dioptre

Hence, one dioptre is the strength of a lens that focal length one meter.

When f is in 1 cm, p = \<\frac1F\> / 100 = 100/ f

So we obtain the recipe to define the relationship in between P and f,

Optical strength (Lens Power)

Optical power is characterized as the degree to which a lens, mirror, or other optical system converges or quarter the light.

Optical power is additionally referred to together the dioptric power, convergence power, refractive power, or refractive power. The is equal to p = \<\frac1F\>.

Diopter Formula

Dioptre formula is used to calculation the optical strength of a lens or bent mirror. The dioptre is the unit for a measure up of the refractive table of contents of a lens. The strength of a lens is stated as the station of the focal length in meters, or D =\<\frac1F\>, wherein D is the strength in dioptres.

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Power the Lens Calculation

Example. Find the power of a plano-convex lens, as soon as the radius that a curved surface ar is 15 cm and v =1.5.