What is the curvature of the wavefront that is created 2 cm to the
right of a +3 D lens when light from the sun is incident on the lens?

To find the curvature of the wavefront created 2 cm to the right of a +3 D lens when light from the sun is incident on the lens, we can follow these steps:

### 1. Understanding the situation:
- The **power** of the lens is \( P = +3 \, \text{D} \) (diopters).
- The **distance** of the point where the curvature is measured is 2 cm to the right of the lens.
- The **incident light** from the sun can be considered as parallel rays, implying the object is at infinity.

### 2. Curvature and Lens Formula:
The curvature of the wavefront is related to the inverse of the radius of curvature of the wavefront. The **lens formula** relates the object distance \( u \), image distance \( v \), and the power of the lens:

\[
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}
\]

Where:
- \( f \) is the focal length of the lens,
- \( u \) is the object distance (since the object is the sun, \( u \approx \infty \)),
- \( v \) is the image distance from the lens.

Given the **power** \( P \) of the lens in diopters is related to the focal length \( f \) by:

\[
P = \frac{1}{f} \quad \text{(in meters)}
\]

Substitute \( P = 3 \, \text{D} \):

\[
f = \frac{1}{3} \, \text{m} = 0.333 \, \text{m} = 33.33 \, \text{cm}
\]

### 3. Finding the Image Distance \( v \):
Since \( u = \infty \) (parallel light), the lens formula simplifies to:

\[
\frac{1}{v} = \frac{1}{f}
\]

So, the image is formed at the focal length:

\[
v = f = 33.33 \, \text{cm}
\]

### 4. Curvature of the Wavefront at 2 cm:
The **curvature** of the wavefront \( C \) is the inverse of the radius of curvature \( R \). Here, the radius of curvature \( R \) is the distance from the image to the point where the wavefront is measured. Since we are measuring 2 cm to the right of the lens, the point is 33.33 cm - 2 cm = 31.33 cm from the image location.

Thus, the curvature is:

\[
C = \frac{1}{R} = \frac{1}{31.33 \, \text{cm}} = \frac{1}{0.3133 \, \text{m}} \approx 3.19 \, \text{m}^{-1}
\]

### Final Answer:
The curvature of the wavefront 2 cm to the right of the +3 D lens is approximately **3.19 m⁻¹**.

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Would you like more details or have any questions? Here are 5 related questions:

1. How does the curvature change if the point is further from the lens?
2. What happens if the lens power is increased to +4 D?
3. How would the curvature be affected if the light source was not at infinity?
4. Can this concept be applied to concave lenses? How would the curvature change?
5. How is focal length affected by the refractive index of the lens material?

**Tip:** The curvature of wavefronts increases as you get closer to the focal point of a converging lens.

What is the curvature of the wavefront that is created 2 cm to the right of a +3 D lens when light from the sun is incident on the lens?

Calculate the curvature of a wavefront created 2 cm behind a +3 D lens when light from the sun is incident on it. Explore the relationship between diopters, lens formula, and wavefront curvature with a step-by-step solution. Suitable for high school physics students.

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