If the focal length of a convex lens is 50 cm, which one of the following is its power?
+2 dioptre
Calculating Convex Lens Power from Focal Length
The question asks us to find the power of a convex lens given its focal length is 50 cm. Understanding the relationship between focal length and lens power is key here.
Understanding Lens Power and Focal Length
The power of a lens is a measure of its ability to converge or diverge light rays. It is defined as the reciprocal of the focal length. The unit of lens power is the dioptre (D).
The formula connecting power (\(P\)) and focal length (\(f\)) is:
\(P = \frac{1}{f}\)
Important Note: In this formula, the focal length (\(f\)) must always be expressed in metres (m).
Sign Convention for Focal Length
- For a convex lens (also known as a converging lens), the focal length is considered positive.
- For a concave lens (also known as a diverging lens), the focal length is considered negative.
Since the question specifies a convex lens, the focal length of 50 cm will be positive.
Step-by-Step Calculation of Lens Power
Let's follow these steps to calculate the power of the convex lens:
- Identify the given focal length.
- Determine the sign of the focal length based on the type of lens.
- Convert the focal length from centimetres to metres.
- Use the formula \(P = \frac{1}{f}\) to calculate the power.
Applying the Steps:
- Given focal length \(f = 50 \text{ cm}\).
- The lens is convex, so the focal length is positive: \(f = +50 \text{ cm}\).
- Convert centimetres to metres: \(1 \text{ m} = 100 \text{ cm}\). \[f = \frac{50}{100} \text{ m} = 0.50 \text{ m}\] So, \(f = +0.50 \text{ m}\).
- Calculate the power using the formula \(P = \frac{1}{f}\): \[P = \frac{1}{+0.50 \text{ m}}\] \[P = +2 \text{ dioptre}\]
The power of the convex lens with a focal length of 50 cm is +2 dioptre.
Comparing with Options
Let's compare our calculated power with the given options:
| Option | Power Value |
|---|---|
| 1 | +2 dioptre |
| 2 | +0.02 dioptre |
| 3 | -0.5 dioptre |
| 4 | +0.5 dioptre |
Our calculated power, +2 dioptre, matches Option 1.
Revision Table: Lens Properties
| Property | Convex Lens | Concave Lens | Relation to Power |
|---|---|---|---|
| Shape | Thicker at center | Thinner at center | N/A |
| Nature of Light Rays | Converging | Diverging | Convergence/Divergence capability is measured by power |
| Focal Length Sign | Positive (\(f > 0\)) | Negative (\(f < 0\)) | \(P = 1/f\) |
| Power Sign | Positive (\(P > 0\)) | Negative (\(P < 0\)) | Sign of P is same as sign of f |
Additional Information: Dioptre and Lens Applications
The unit dioptre simplifies calculations involving lens power. If lenses are placed in contact, their total power is simply the sum of their individual powers (\(P_{total} = P_1 + P_2 + ...\)). This is why optometrists use dioptres when prescribing corrective lenses.
Corrective lenses for vision problems use the concept of power:
- Myopia (nearsightedness) is corrected using concave lenses, which have negative power and diverge light before it reaches the eye's lens.
- Hyperopia (farsightedness) is corrected using convex lenses, which have positive power and converge light more strongly.
The power of a lens is inversely proportional to its focal length. This means a lens with a shorter focal length will bend light more strongly and have a higher power.
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