Power of a Lens Ray Optics - Definition, Formula, FAQs

Edited By Vishal kumar | Updated on Sep 24, 2024 10:05 PM IST

In this article we are going to discuss about a very important topic of class 10, power of lens, power of a lens formula, diopter formula, what is power of lens, ray optics formula, how to find a power of lens, relation between power and focal length, optical power, and many more.
So , we will start with what is lens and what are the sign conventions used in lens .

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Power of a Lens Ray Optics - Definition, Formula, FAQs

What is lens?

Lens is a transparent magnifying curved glass through which light rays converged or diverges. There are two types of lenses namely concave lens and convex lens .

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Power of a lens

We know that a convex lens converges the light rays incident on it but a concave lens diverges the incident light rays the power of a lens is a measure of its ability to converge or diverge light rays that incident on it .

This ability is based on its focal length . It is found that a convex lens of shorter focal length bends the light rays through larger angles and focusses them closer to the optical centre. Similarly a concave lens of smaller focal length produces more divergence than a lens of longer focal length. This shows that the power of lens is inversely proportional to the focal length of the lens.

From this considerations ,

Power of a lens formula / power of lens formula

The power of a lens is mathematically defined as the reciprocal of its focal length.

Power of a lens (p) = 1 / focal length of lens (f)

P = 1 / f

This is how to find power of lens . This is the relation between power and focal length .

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Diopter formula

Si unit of power of a lens

Si unit of the power of lens is dioptre. It is usually denoted by the letter ‘d’ .

If focal length f of a given lens is 1m , then as per relation of power of a lens formula

P = 1 / (1 m focal length) = 1 dioptre = 1 d

It means that ,

If focal length of a lens is f metre , then its power lens formula is given as :

P = 1 / f ( in m )

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Since , focal length of a convex lens is positive and that of a convex lens is negative . Hence , accordingly the power of a convex ( converging ) lens is taken to be positive and the power of a concave lens ( diverging ) lens is taken to be negative .

Opticians prescribe corrective lenses for defects of vision indicating their powers . For ex , if an optician prescribes a power +2.0 d

To a person , then +ve sign of power means that the lens is a convex lens and its focal length is

F = 1 / p = 1 / 2.0 m or 50 cm .

Similarly , a lens of power – 0.5 d means a concave lens of a focal length is equal to 200 cm .

Optical power formula of a combination of two or more thin lenses in contact

If a number of thin lenses are placed in contact , then the resultant power of lens combination is equal to the algebraic sum , of the powers of individual lenses . If two thin lenses of power p1 and p2 are placed in contact with each other , then resultant power p is given as :

P = p1 + p2

For more than 2 lenses of powers p1 ,p2 ,p3 , p4 …

Then the resultant power p is given as :

P = p1 + p2 +p3 + p4 …

In terms of focal lengths , it may be expressed as :

1/f = 1/f1 + 1/f2 + 1/f3 + 1/f4 …

Here , f1, f2, f3, f4, are the focal length of individual lenses in contact and f is the resultant focal length of lens combination . Hence , this is how to find power of lens using focal length .

So at last we have discussed about power of lens, power of a lens formula, diopter formula, what is power of lens, ray optics formula, how to find a power of lens, relation between power and focal length, optical power.

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Frequently Asked Questions (FAQs)

1. What are the sign conventions to lens for using optical formula.

The sign conventions used for spherical lenses if the object is always placed to the left of the lens so that the light from the object falls to the lens from the left hand side

Oldest census parallel to the principal axis usually called x-axis are measured from optical lens is taken as the origin point

All distance is measured to the right of the origin along x axis are taken as positive but distance is measured to the left of the origin are taken as negative

Along the direction perpendicular to the principal axis usually called y- axis heights measured above the principal axis are taken as positive but height measured below the principal axis are taken as negative.

2. How to check power of a lens at home .

Lensometer is usually used in optical shops and hospital use.

3. Ray optics formula of class 12.

Ray optics formulas are

Total internal refraction	n1n2 = sin(r) sin(i). n1n2=sin(r)sin(i)
Critical angle, θ	sinθ=n2n1sinΘ=n2n1
Prism formula	μ=sinA+δm2sinA2μ=sinA+δm2sinA2
Lens maker formula	1f=(μ−1)(1R1−1R2)

4. What is linear magnification of lens.

Magnification produced by a lens gives the relative extent to which the image of an object is enlarged or diminished with respect to the object size for a linear object held normal to the principal axis of a spherical lens. The linear magnification or magnification is represented as the ratio of the image height to the object height.

M = h’/h

Magnification produced by a lens is represented in terms of distance of the object and the distance of the image. It is given by:

M = v/u.

5. Use of additive property of lenses.

Additive property of power of lenses is also used to design lens system so as to minimised search images produced by a single lens is commonly used in design of camera lenses and lenses of microscopes and telescopes this property is very convenient for opticians during eye testing.