Which of the following lenses will bend the light rays through the largest angle?
Lens with power +2·5 D
Understanding Lens Power and Light Bending
The ability of a lens to bend light rays is measured by its power. The greater the power of a lens, the more it will bend the light rays passing through it. Lens power is typically measured in Diopters (D).
The power (P) of a lens is related to its focal length (f) by the formula:
\(P = \frac{1}{f}\)
where \(f\) is in meters.
A positive power indicates a converging lens (like a convex lens), which bends parallel light rays inwards towards a focal point. A negative power indicates a diverging lens (like a concave lens), which bends parallel light rays outwards away from a focal point.
The extent to which a lens bends light rays, or the angle of bending, depends on the magnitude of its power. A higher magnitude of power, regardless of whether it's positive or negative, means a shorter focal length and thus a greater bending effect on the light rays.
Comparing Lens Powers and Bending Angle
We are given four lenses with different powers:
- Lens 1: Power = +2.0 D
- Lens 2: Power = +2.5 D
- Lens 3: Power = -1.5 D
- Lens 4: Power = -2.0 D
To find which lens bends light through the largest angle, we need to compare the magnitudes of their powers.
Let's find the magnitude of power for each lens:
- Lens 1: Magnitude of power = \(|+2.0|\) D = 2.0 D
- Lens 2: Magnitude of power = \(|+2.5|\) D = 2.5 D
- Lens 3: Magnitude of power = \(|-1.5|\) D = 1.5 D
- Lens 4: Magnitude of power = \(|-2.0|\) D = 2.0 D
Now, let's compare these magnitudes:
| Lens | Given Power (D) | Magnitude of Power (D) |
|---|---|---|
| Lens 1 | +2.0 | 2.0 |
| Lens 2 | +2.5 | 2.5 |
| Lens 3 | -1.5 | 1.5 |
| Lens 4 | -2.0 | 2.0 |
Comparing the magnitudes of power (2.0 D, 2.5 D, 1.5 D, and 2.0 D), we see that the largest magnitude is 2.5 D. This corresponds to the lens with a power of +2.5 D.
Determining the Lens with Largest Bending
Since the lens with the power of +2.5 D has the largest magnitude of power (2.5 D), it means this lens has the shortest focal length (in magnitude: \(|f| = 1/|P| = 1/2.5 = 0.4\) meters). A shorter focal length indicates a stronger lens that bends light rays more significantly.
Therefore, the lens with power +2.5 D will bend the light rays through the largest angle compared to the other lenses listed.
Revision Table: Key Optics Concepts
| Concept | Description | Relation to Bending |
|---|---|---|
| Lens Power (P) | Measure of a lens's ability to converge or diverge light. Unit: Diopter (D). | Higher magnitude of power means greater bending. |
| Focal Length (f) | Distance from the lens center to the focal point. | Shorter focal length (magnitude) means higher power and greater bending. \(P = 1/f\). |
| Converging Lens (+P) | Bends light rays inwards. Example: Convex lens. | Bending towards the principal axis. |
| Diverging Lens (-P) | Bends light rays outwards. Example: Concave lens. | Bending away from the principal axis. |
Additional Information: Types of Lenses and Bending
Lenses are broadly classified into two types:
1. Converging Lenses (Convex Lenses):
- These lenses are thicker in the center than at the edges.
- They have a positive power (+D).
- They converge parallel light rays to a real focal point.
- The amount of convergence (inward bending) is determined by the magnitude of the positive power.
2. Diverging Lenses (Concave Lenses):
- These lenses are thinner in the center than at the edges.
- They have a negative power (-D).
- They diverge parallel light rays as if they are coming from a virtual focal point.
- The amount of divergence (outward bending) is determined by the magnitude of the negative power.
In both cases (converging and diverging), the absolute value (magnitude) of the power determines the strength of the lens and how much it bends light. A lens with a power of +5 D bends light just as much, but in the opposite direction, as a lens with a power of -5 D.
This question asks about the largest angle of bending, which relates directly to the strength or magnitude of the power. The sign only tells us the direction of bending (inwards or outwards).
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