Power of a Lens MCQs Quiz | Class 10
This quiz covers Class X Science (Code 086), Unit III: Natural Phenomena, focusing on the topic of Power of a Lens, including its definition, the unit dioptre, and its relation with focal length. Test your understanding by answering these multiple-choice questions and then download your personalized answer PDF.
Understanding Power of a Lens
The power of a lens is a fundamental concept in optics, quantifying its ability to converge or diverge light rays. It is essential for designing optical instruments and corrective lenses. This section explores the definition of lens power, its standard unit, and its crucial relationship with the focal length.
1. Definition of Power of a Lens
The power of a lens (P) is defined as the reciprocal of its focal length (f) when the focal length is expressed in metres. It indicates how much a lens can bend light. A lens with a higher power bends light more significantly.
- Positive Power: Corresponds to a converging (convex) lens, which focuses parallel light rays to a real focus.
- Negative Power: Corresponds to a diverging (concave) lens, which spreads out parallel light rays as if they originated from a virtual focus.
2. Unit Dioptre (D)
The standard international (SI) unit for the power of a lens is the dioptre (D). One dioptre is defined as the power of a lens whose focal length is one metre (1 D = 1 m-1). Therefore, to calculate power in dioptres, the focal length must always be substituted in metres.
For example, if a lens has a focal length of 25 cm, it must first be converted to 0.25 m. Its power would then be P = 1 / 0.25 m = +4 D.
3. Relation with Focal Length
The mathematical relationship between the power (P) of a lens and its focal length (f) is inverse:
P = 1 / f
Where:
- P is the power in dioptres (D).
- f is the focal length in metres (m).
Key implications of this relationship:
- A lens with a shorter focal length has a greater power, meaning it converges or diverges light more strongly.
- Conversely, a lens with a longer focal length has a smaller power, indicating a weaker ability to bend light.
Summary of Lens Properties and Power
| Lens Type | Focal Length (f) | Power (P) | Nature of Lens |
|---|---|---|---|
| Convex Lens | Positive | Positive | Converging |
| Concave Lens | Negative | Negative | Diverging |
Quick Revision Points
- Power of a lens (P) quantifies its ability to converge or diverge light.
- Formula: P = 1 / f, where ‘f’ must be in metres.
- The SI unit of power is the dioptre (D).
- Convex lenses have positive focal length and thus positive power.
- Concave lenses have negative focal length and thus negative power.
- Greater power implies a shorter focal length and stronger bending of light.
Practice Questions
- Calculate the power of a lens if its focal length is +20 cm.
- A person is prescribed spectacles with a power of -1.5 D. What is the focal length of the lens and what type of lens is it?
- Why do ophthalmologists specify lens power in dioptres rather than focal length?
- What is the power of a plane glass sheet? Justify your answer.
- If two lenses, one with P1 = +3D and another with P2 = -1D, are combined, what is the power of the combination?
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