Power of a lens of focal length 25 cm is
+4 Diopter
Calculating Lens Power from Focal Length
The question asks for the power of a lens with a given focal length. The power of a lens is a measure of how strongly it converges or diverges light. It is directly related to the focal length of the lens.
Understanding Lens Power and Focal Length
- Focal Length (f): This is the distance from the optical center of the lens to the principal focus where parallel rays of light converge (for a converging lens) or appear to diverge from (for a diverging lens). It is typically measured in meters (m) or centimeters (cm).
- Lens Power (P): This is the reciprocal of the focal length when the focal length is measured in meters. The unit of lens power is the Diopter (D). One Diopter is equivalent to one reciprocal meter ($$1/m$$).
The Formula for Lens Power Calculation
The relationship between lens power and focal length is given by the formula:
$$ P = \frac{1}{f} $$
Where:
- $$P$$ is the power of the lens in Diopters (D).
- $$f$$ is the focal length of the lens in meters (m).
It is crucial that the focal length is in meters when using this formula to get the power in Diopters.
Step-by-Step Calculation for 25 cm Focal Length
We are given the focal length of the lens as 25 cm. To use the power formula, we must convert this value to meters.
We know that $$1 \text{ meter} = 100 \text{ centimeters}$$.
So, to convert centimeters to meters, we divide by 100:
$$ f = 25 \text{ cm} = \frac{25}{100} \text{ m} = 0.25 \text{ m} $$
Now, we can use the formula for lens power:
$$ P = \frac{1}{f} $$
Substitute the focal length in meters:
$$ P = \frac{1}{0.25 \text{ m}} $$
Calculating the value:
$$ P = 4 \text{ D} $$
The focal length given (25 cm) is positive, which corresponds to a converging lens. A converging lens has positive power.
Analyzing the Options
Let's compare our calculated power with the given options:
| Option | Power Value |
|---|---|
| 1 | $$+2.5 \text{ Diopter}$$ |
| 2 | $$+3 \text{ Diopter}$$ |
| 3 | $$+4 \text{ Diopter}$$ |
| 4 | $$+5 \text{ Diopter}$$ |
Our calculated power is $$+4 \text{ Diopter}$$, which matches Option 3.
Summary of Lens Power Calculation
To find the power of a lens from its focal length:
- Ensure the focal length is in meters. Convert from centimeters if necessary ($$f_{\text{meters}} = f_{\text{centimeters}} / 100$$).
- Use the formula $$P = 1/f$$ to calculate the power in Diopters.
Revision Table: Lens Properties
| Property | Converging Lens (Convex) | Diverging Lens (Concave) |
|---|---|---|
| Focal Length (f) | Positive | Negative |
| Power (P) | Positive | Negative |
| Effect on parallel rays | Converges them to a point | Diverges them as if from a point |
Additional Information on Lens Power and Applications
Lens power is a very practical concept, especially in ophthalmology and corrective lenses. Eyeglasses and contact lenses are prescribed in terms of their power in Diopters. A positive power indicates a converging lens used to correct farsightedness (hyperopia), while a negative power indicates a diverging lens used to correct nearsightedness (myopia).
The unit Diopter is named after the French ophthalmologist Ferdinand Monoyer, who proposed it in 1872. Using power instead of focal length makes it easier to calculate the combined effect of multiple lenses in contact; their powers simply add up ($$P_{\text{total}} = P_1 + P_2 + P_3 + ...$$).
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