

What is the Power of a Lens?
The ability of a lens to bend the light falling on it is called the power of a lens. Since the lens of shorter focal length will bend the light rays more will have more power. A convex lens converges the light rays towards the principal axis whereas a concave lens diverges the light rays away from the principal axis.
Here,
\[P=\frac{1}{F}\]
The power of a lens is defined as the inverse of its focal length (f) in meters (m).
Power of a Lens Formula Definition
The power of a lens is specified as \[P=\frac{1}{F}\], where f is the focal length.
The S.I. unit of power of a lens is \[m^{-1}\]. This is also known as diopter.
The focal length (f) of a converging lens is considered positive and that of a diverging lens is considered negative. Thus, the power of a converging lens is positive and that of the diverging lens is negative.
Lens Formula in Terms of Power
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Fig.1 shows two lenses L1 and L2 placed in contact. The focal lengths of the lenses are f1 and f2, respectively. Let P be the point where the optical centres of the lenses coincide (lenses being thin).
Now, let us place an object ‘O’ beyond the focus of lens L1 such that OP = u (object distance) on the common principal axis (coaxially).
Here, the first lens L1 alone forms an image at I1 where PI1 = v1 (image distance).
Also, this point I1 works as the virtual object for the second lens L2 and the final image is formed at I, at a distance PI = v. The ray diagram (Fig.1) formed by the combination of two convex lenses has the following attributes:
u = Object-distance for the first lens
v = final image-distance for the second lens
v1 = image-distance for the first image I1 for the first lens. As the lenses are pretended to be thin, v1 is also the object distance for the second lens.
The lens formula for the image I1 formed by lens L1 will be
\[\frac{1}{v_1}-\frac{1}{u}=\frac{1}{F}\].....(1)
The equation for the image formation for the second lens L2:
\[\frac{1}{v}-\frac{1}{v_1}=\frac{1}{f_2}\].....(2)
Adding eq (1) and (2):
\[\frac{1}{v_1}-\frac{1}{u}+\frac{1}{v}-\frac{1}{v_1}=\frac{1}{F_1}+\frac{1}{f_2}\]
\[\frac{1}{v}-\frac{1}{u}=\frac{1}{F_1}+\frac{1}{f_2}\].....(3)
The focal length of the combined lens is given by-
If the combination is replaced by a single lens of focal length F such that it forms the image of O at the position I,
1/v - 1/ u = 1/ F……(4)
This type of lens is called the equivalent lens for the combination.
Combining (3) and (4),
1/F = 1 / f1 + 1/ f2……(5)
Here, F is the focal length of the equivalent lens for the combination. As the power of a lens is P = 1/ F, eq (5) immediately gives,
The power of any number of lenses in contact is equal to the algebraic sum of the power of two individual lenses. This is true for any situation involving two thin lenses in contact.
How to Find the Power of the Lens Using the Focal Length?
The power of a lens is measured as the reciprocal of the focal length of the lens.
Relation with focal length: A lens of less focal length produces more converging or diverging and is said to have more power.
I.e.,
According to the lens maker’s formula,
Since, P = 1/ F
We get,
Here,
v = refractive index of the material
R1 = Radius of curvature of the first surface of the lens
R2 = Radius of curvature of the second surface of the lens
For a converging lens, power is taken as positive and for a diverging lens, power is taken as negative.
Definition for the Power of Lens Unit
The S.I. the unit of power is dioptre (D).
When f = 1 meter, P = 1/ f = 1/ 1 = 1 dioptre
Hence, one dioptre is the power of a lens of focal length one meter.
When f is in 1 cm, P = 1/ f / 100 = 100/ f
So, we get the formulas to describe the relationship between P and f,
Optical Power (Lens Power)
Optical power is defined as the degree to which a lens, mirror, or other optical system converges or diverges the light. Optical power is also referred to as dioptric power, convergence power, refractive power, or refractive power. It is equal to P = 1/ f.
Dioptre Formula
The Dioptre formula is used to calculate the optical power of a lens or curved mirror. The dioptre is the unit for a measure of the refractive index of a lens. The power of a lens is specified as the inverse of the focal length in meters, or D =1/ f, where D is the power in dioptres.
Power of Lens Calculation: Solved Example
1. Find the power of a plano-convex lens, when the radius of a curved surface is 15 cm and v =1.5.
Solution: Given R1 = ∞, R2 = - 15 cm, v= 1.5 cm
P = \[\frac{1}{f}=(v-1)(\frac{1}{R_1}-\frac{1}{R_2})\]
= (1.5-1)\[(\frac{1}{\infty }+\frac{1}{0.15})\]
= 0.5\[\times \frac{1}{0.15}=3.33\]
From the above formula for the power of the lens, we understand that the power of a lens is the reciprocal of the focal length (which we calculate in metres). Lens power is measured in dioptres (D), which is also equal to 1/m.
Converging (convex) lenses have positive focal lengths, so they also have positive power values. However, diverging (concave) lenses have negative focal lengths, so they also have negative power values.
FAQs on Power of a Lens
1. What is the power of a lens as per the CBSE Class 10 and 12 syllabus?
The power of a lens is a measure of its ability to converge or diverge light rays that pass through it. In simple terms, it quantifies how much a lens can bend light. A lens with a higher power bends light more strongly. According to the NCERT curriculum for the 2025-26 session, this concept is crucial for understanding optical instruments.
2. What is the fundamental formula used to calculate the power of a lens?
The power (P) of a lens is calculated as the reciprocal of its focal length (f) when the focal length is measured in metres. The standard formula is:
P = 1 / f (where f is in metres)
This relationship is a cornerstone of the chapter on Light - Reflection and Refraction.
3. How is the power of a lens inversely related to its focal length?
The power of a lens is inversely proportional to its focal length. This implies:
- A lens with a shorter focal length has a higher power because it bends light more sharply to a closer focal point.
- A lens with a longer focal length has a lower power as it bends light less aggressively over a greater distance.
4. What is a dioptre, the SI unit for the power of a lens?
One dioptre (D) is the standard SI unit of power for a lens. It is officially defined as the power of a lens that has a focal length of exactly one metre (1m). Therefore, a +2D lens is a convex lens with a focal length of 0.5 metres.
5. How do you calculate the power of a lens if the focal length is given in centimetres (cm)?
When the focal length (f) is provided in centimetres, you can use a modified formula for convenience. Instead of converting cm to m first, you can directly calculate the power (P) using:
P = 100 / f (where f is in cm)
This is a common conversion used in solving numerical problems.
6. Why is the power of a convex lens considered positive, while a concave lens is negative?
The sign convention is directly linked to the focal length of the lens:
- A convex lens is a converging lens, which, by Cartesian sign convention, has a real and positive focal length. Since P = 1/f, its power is also positive.
- A concave lens is a diverging lens, which has a virtual and negative focal length. Consequently, its power is also negative.
7. How do you find the total power when multiple thin lenses are placed in contact?
For a combination of two or more thin lenses placed in direct contact, the total or equivalent power is the simple algebraic sum of the individual powers of the lenses. The formula is:
P_total = P₁ + P₂ + P₃ + ...
For example, combining a +3D lens with a -1D lens results in a total power of +2D.
8. Which type of lens has more power, a thick one or a thin one, and why?
A thick lens generally has more power than a thin lens of the same material. This is because a thicker lens typically has surfaces with a greater curvature. According to the Lens Maker's formula, a greater curvature leads to a shorter focal length. Since power is the reciprocal of focal length (P = 1/f), a shorter focal length results in a higher power value.
9. How does the power of a lens relate to its real-world application in eyeglasses?
In eyeglasses, the power value indicates the degree of vision correction required. A higher numerical value signifies a stronger correction.
- Positive power (e.g., +2.5D) is used in convex lenses to correct hypermetropia (farsightedness).
- Negative power (e.g., -3.0D) is used in concave lenses to correct myopia (nearsightedness).

















