Dimensions of Power of Lens

# Dimensions of Power of Lens

A lens is really a transparent material, usually glass, that is used to focus or disperse a light beam. This makes use of light’s refraction property. The transition in the path of light observed when it travels from one medium to another is referred to as refraction. The lens directs the light to a single point and creates the image. This is primarily used as a contact lens in our spectacles, magnifying glasses, microscopes, and other similar devices. One of the most fascinating concepts in ray optics is the Power of a Lens. The potential of a lens to bend light is what gives it its power. The bigger the strength of a lens, the better its ability to refract light passing through it. Power describes a convex lens’s capacity to converge and a concave lens’s ability to diverge. As the focal length decreases, the number of light bends increases. As an outcome, we can deduce that a lens’s strength is inversely proportional to its focal length. In essence, a short focal length leads to high optical power.

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In Ray Optics, the formula P = 1/ F can be used to calculate the power of a lens.

If indeed the focal length is given in meters (m), the power of the lens is measured in Diopters (D), as the lens’s unit of power is diopter. Some other thing to remember is that the optical power of a converging lens is positive, whereas the optical power of a diverging lens is negative. For instance, if the focal length of a lens is 20 cm, we get 0.2 m when we convert it to meters. Consider taking the reciprocal of 0.2 to get the power of this lens, which is 5. As a result, the power of this lens is 5D.

The focal length of a lens seems to be inversely proportional to its power. As a result, a lens with a short focal length has more power, whereas a lens with a long focal length has less power.

• A convex lens (converging lens) has a positive power because its focal length is positive.
• A concave lens (diverging lens) has a negative power because its focal length is negative.
• A plane glass plate has a power of 0.

Optometry is really a significant application of using lens power. Optometrists recommend corrective lenses (convex or concave) based on deteriorating vision. One’s eye is essentially a lens, and you may occasionally have difficulty seeing clearly. Wearing corrective lenses with the appropriate power can help to correct this.

## Dimensional Formula of Power of Lens

The dimensional formula of Power of Lens can be represented as:

[M0 L-1 T0]

Here,

M = Mass

L = Length

T = Time

## Derivation:

We have, Power of Lens (D) = Focal Length-1 . . . (1)

Now, the dimensional formula of focal length = [M0 L1 T0] . . . . (2)

When substituting equation (2) in equation (1) we get,

Power of Lens = Focal Length-1

That is, D = [M0 L1 T0]-1 = [M0 L-1 T0].

Thus, the power of lens has been dimensionally represented as [M0 L-1 T0].

## FAQs

##### What are the dimensions of power?

Power has been defined as energy divided by time and the unit of power in the International System of Units (SI) is the watt (W), which is equal to one joule per second.

##### What is dimension of focal length?

The focal length of a lens is indeed the distance between the lens and the image sensor when the subject is in focus, and it is usually expressed in millimetres.

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