Dimensional Formula of Power of Lens

The term power of a lens signifies its capacity to bend the light (converge or diverge) that falls on it. A lens of a shorter focal length tends to bend light rays more and has more power. The lens with a longer focal length will have the opposite nature of less bending of light and less power. The light rays of a convex lens converge towards the principal axis, whereas the light rays of a concave lens diverge away from the principal axis. The nature of the lens depends upon the refracting index of the surrounding area. The SI unit is dioptre(D).

Power of lens formula

• The power of the lens formula can be defined as the reciprocal of its focal length.
• The formula is-

                          D =1/f 

Where D = it is the power in diopters.

               f = focal length in metres.

• dioptre D or m^–1 is the SI unit of the power lens.
• The power of the concave lens is negative because it is a diverging lens. 
• The power of the convex lens is positive because it is a converging lens. 
• The power of the combination of a lens can be defined when more than one lens is used together; it is called the power of the combination of the lens.

Dimensional formula of power of the lens

The power of the lens is the ability of the lens to deviate the parallel lights towards or away ( converge or diverge) principle axis, and mathematically it is termed the inverse of focal length.

The dimensional formula of Power of Lens is written as:

[M⁰L^–1T⁰]

Where,

M: Mass

L: Length

T: Time

Derivation for the dimensional formula of power of lens

Power of Lens (D) = 1 / (Focal Length)

• D = 1 / (F)

Power is expressed in Dioptre (D). …(i)

• The dimensional formula of focal length = [M⁰L¹T⁰] …(ii)

From the following equations (i) and (ii)

Power of Lens = 1 / (Focal Length) i.e (D) = (F)-1

• Therefore, D = [M⁰L¹T⁰]^-1 = [M⁰L–¹T⁰]

Hence, the dimensional formula of the power of lens can be written as:

[M⁰L^-1T⁰]

Dimensional formula

In terms of dimensions, a dimensional formula is an equation that expresses the relationship between fundamental and derived units (equation). The letters L, M, and T are used to represent the three basic dimensions of length, mass, and time in mechanics.

All physical quantities can be stated in terms of the fundamental (base) units of length, mass, and time, multiplied by some factor (exponent).

The dimension of the amount in that base is the exponent of a base quantity that enters into the expression.

The units of fundamental quantities are expressed as follows to determine the dimensions of physical quantities:

• ‘L’ stands for length, 
• ‘M’ for mass, and 
• ‘T’ for time.

Example: The area is equal to the sum of two lengths. As a result, [A] = [L²]. That is, an area has two dimensions of the length and zero dimensions of mass and time. In the same way, the volume is the sum of three lengths. As a result, [V] = [L³]. That is, the volume dimension has three dimensions: length, mass, and time.

Conclusion

The power of the lens is the ability of a lens to bend the parallel lines into converging or diverging to form a picture. The lens is of two types concave and convex. The nature of the lens depends upon the surrounding medium it is submerged into, i.e. the refractive index of the external medium material can be less, more or equivalent, which will affect the nature of the lens accordingly ( inverse, same or as a plane mirror respectively).

The dimensional formula of the power of lens can be written as:

[M⁰L^-1T⁰]

The dimensional formula of focal length = [M⁰L¹T⁰]