Muskan Shafi Education Content Expert
Education Content Expert
Power of a Lens is the ability of a spherical lens to bend the light falling on it. The focal length of a lens defines its ability to converge or diverge the light rays. Power of a Lens determines the refractive properties of a lens.
- The power of a concave lens is negative while the power of a convex lens is positive.
- The convergence of light rays by a convex lens is towards the principal axis.
- The divergence of light rays by a concave lens is away from the principal axis.
- Power of a Lens is the reciprocal of the focal length of the lens.
Power of a Lens is given by the formula:
| \(P = {1 \over f}\) |
Here, P is the power of a lens and f is the focal length of the lens.
Read More: NCERT Solutions for Class 10 Science Light- Reflection and Refraction
Key Terms: Power of a Lens, Lens Maker’s Formula, Focal Length, Dioptre, Light, Refraction, Concave Lens, Convex Lens, Optometry
Power of a Lens
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Power of a Lens is defined as the ability of a lens to bend the light rays falling on it. A shorter focal length bends more light and a longer focal length bends less light.
- The SI unit of Power of a Lens is ‘Dioptre’ (D).
- Concave lenses have a negative power while the power of a convex lens is positive.
- Power of a Lens is calculated as the reciprocal of the focal length of the lens.
- Optical power is the ability of optical instruments such as spherical mirrors or lenses to converge or diverge light.
- Optical power is also known as convergence power, refractive power, or dioptric power.
- ‘Optometry’ is the field in which the power of a lens is used to make corrective lenses based on depreciating vision.
Spherical Lenses
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Power of a Lens Formula
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In Ray Optics, Power of a Lens is the reciprocal of the focal length of the lens. Thus, Power of a Lens Formula is given as follows:
| \(P = {1 \over f}\) |
Where
- P is the Power of a Lens.
- f is the focal length of the Lens. (In meters)
Thus, there is an inverse relationship between the focal length and the power of a lens. A lens with a short focal length will have more power, while a lens with a long focal length will have less power.
- Convex Lens has a positive power because its focal length is positive.
- Concave Lens has a negative power because its focal length is negative.
- A plane glass plate has zero power.
Thus, if a lens of power has a power of +2.0 D, then it will be a convex lens and if the power is -2.5 D then that lens is concave.
Solved ExampleExample: Find the power of a lens whose focal length is 80 cm. What will be the type of lens used? Solution: The focal length of the lens is given as 80 cm (0.8 m). Using the Power of a Lens Formula, P = 1/f P = 1/0.8 P = 10/8 = 1.25 D The power of the lens and the focal length is positive, thus, the lens used is a convex lens. |
Some of the optical instruments have many lenses combined to get better sharpness and magnification of the image. In that case, the net power (P) of the combined lenses is given by adding the individual power of the lenses. This will be done in any case even when two thin lenses have been combined together.
Suppose the power of the individual lens is given as P1, P2, P3, …etc, then the net power (P) will be calculated as
| P = P1 + P2 + P3 + … Pn |
Read More: Image Formation by Lenses
Unit of Power of a Lens
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The SI unit of the power of a lens is Dioptre (D). One dioptre is the power of a lens whose focal length is one meter.
- When f = 1 meter, P = 1/ f = 1/ 1 = 1 Dioptre
- When f = 1 cm, P = 1/ f / 100 = 100/ f
Thus, Power of a Lens will be given as
- P (Dioptre) = 1 / f (Meter)
- P (Dioptre) = 100 / f (Centimeter)
Read More: Light-Reflection and Refraction Important Questions
What is Focal Length?
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Focal Length of a Lens is a degree of how sharply light is converged or diverged. Whenever light passes through a lens after coming from infinity, the point at which it converges is known as the ‘Focal Point’. It is denoted by ‘F’.
- Focal length is the distance between the pole and the focal point of the lens.
- It is denoted by the letter ‘f’.
- It can be negative or positive, depending on where the focal point is located.
- If the focal point of a lens is located on the opposite side of the lens from the object, it is a positive focal length.
- If the focal point of a lens is located on the same side of the object, it is a negative focal length.
- A concave lens has a negative focal length while a convex lens has a positive focal length.
Lens Maker's Formula
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Lens Maker’s Formula states the relationship between the focal length, refractive index, and radius of curvature of the two spheres used to make the lenses. It is used to manufacture lenses of the desired focal length.
Lens Maker’s Formula is given as
| \(\frac 1f = (v-1) \left( \frac {1}{R_1}- \frac {1}{R_2} \right) \) |
Where
- v is the refractive index of the material.
- f is the focal length.
- R1 is the radius of curvature of the first lens.
- R2 is the radius of curvature of the second lens.
Now, as per the Power of a Lens Formula,
P = 1/f
Therefore, we get
| \(P= (v-1) \left( \frac {1}{R_1}- \frac {1}{R_2} \right) \) |
Thus, the power of a lens can also be calculated if we know the values of the refractive index and radius of curvature of the two lenses.
The video below explains this:
Lens Maker’s Formula Detailed Video Explanation:
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Things to Remember
- Power of a Lens is defined as the ability of a lens to bend the light rays.
- It is the reciprocal of the focal length of a lens.
- Dioptre is the unit of Power of a Lens.
- Concave Lenses have a negative power while convex lenses have positive power.
- Power of a Lens Formula is given as \(P = {1 \over f}\).
- Optometry is the field where the power of the lens is determined to make corrective lenses for vision problems.
Sample Questions
Ques. What is Power of a Lens? Define its SI unit. (2 Marks)
Ans. Power of a lens is defined as the ability of a lens to bend the light rays falling on it. It is the ability of a lens to converge and diverge the light rays. The power of a lens is the reciprocal of the focal length of the lens. Its SI unit is ‘Dioptre’. ‘Dioptre’ is denoted by the letter D.
Ques. A student uses two lenses of focal lengths 40 and -20 cm. Write the nature and power of each lens. (3 Marks)
Ans. Lens with Focal Length 40 cm: In the case of a convex lens, the focal length is positive.
f = 40 cm = 40/100 = 0.40 m
Power of the Lens = 1/f = 1/0.40 = + 2.5 D
So, a lens with a focal length of 40 cm is convex with a power of + 2.5 D.
Lens with Focal Length -20 cm: In the case of a concave lens, the focal length is negative.
f = -20 cm = -20/100 = -0.20 m
Power of the Lens = 1/f = – 1/0.20 = – 5 D
So, a lens having a focal length of -20 cm is concave with a power of -5 D.
Ques. Which lens is considered more powerful, a thin lens or a thick one? (1 Mark)
Ans. The power of a lens is dependent upon its focal length and curvature. A thick lens has a shorter focal length and greater curvature, therefore, a thick lens is more powerful.
Ques. What is Optical Power? (2 Marks)
Ans. Optical Power is the same as the Power of a Lens. It is defined as the degree to which a lens, mirror, or any other optical instrument can converge or diverge the light rays falling on it. It is also known as dioptric power, convergence power, refractive power, or refractive power. Optical Power is given as P = 1/ f.
Ques. What will be the focal length of a lens if its power is -2.25 D? (3 Marks)
Ans. The power of the lens is given as –2.25 D.
Using the Power of a Lens Formula,
P = 1/f
f = 1/P
f = 1/–2.25
f = – 100/225
f = – 4/9
f = – 0.44 m = – 44 cm
Thus, the focal length of the lens is – 44 cm.
Ques. What factors affect the Power of a Lens? (1 Mark)
Ans. The power of a lens is mainly dependent upon the focal length and curvature. A shorter focal length will bend more light and a longer focal length will bend less light.
Ques. What is Lens Maker’s Formula? (3 Marks)
Ans. The Lens Maker’s Formula is given as
\(\frac 1f = (v-1) \left( \frac {1}{R_1}- \frac {1}{R_2} \right) \)
Here,
- f is the focal length.
- v is the refractive index of the given material.
- R1 is the radius of curvature of the first sphere.
- R2 is the radius of curvature of the second sphere.
Ques. What is the application of Power of a Lens? (2 Marks)
Ans. Power of a Lens is very integral in the field of ‘Optometry”. It is used by optometrists to prescribe corrective lenses, either convex or concave lenses, based on the depreciating vision of the person. Vision problems can be corrected by wearing corrective lenses with the appropriate power.
Ques. If a convex lens is placed in front of the eye of a person seeing an extended object. How will the person feel? (1 Mark)
Ans. A convex lens is used for magnifying an object for a clear view. Therefore the person seeing the object will feel that the size of the extended object has magnified or increased.
Ques. What do you mean by positive and negative focal lengths? (3 Marks)
Ans. The focal length of a lens can be positive or negative depending on where the focal point is located.
- Positive Focal length: The focal point with a positive focal length is the one located on the opposite side of the lens. A concave lens has a negative focal length.
- Negative Focal Length. The focal point with a negative focal length is the one located on the same side of the object. Convex lenses have a positive focal length.
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