A spherical air bubble in water will act as

Options

A. a convex lens
B. a concave lens
C. Plane glass plate
D. Plano-concave lens

Answer

To determine how a spherical air bubble in water will act, we can analyze it using the lensmaker's formula. Here’s a step-by-step solution:

### Step 1: Understanding the System
We have a spherical air bubble in water. The refractive index of air (μ_air) is approximately 1, and the refractive index of water (μ_water) is approximately 1.33 (or 1.44 depending on the source).

### Step 2: Applying the Lensmaker's Formula
The lensmaker's formula is given by:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]
Where:
- \( f \) is the focal length,
- \( \mu \) is the refractive index of the medium (in this case, the air bubble),
- \( r_1 \) and \( r_2 \) are the radii of curvature of the bubble.

### Step 3: Identifying the Radii of Curvature
For a spherical bubble:
- Let’s assume \( r_1 \) is the radius of the bubble facing the water and \( r_2 \) is the radius of the bubble facing the air. Since the bubble is spherical, \( r_1 = r \) and \( r_2 = -r \) (the negative sign indicates that the second radius is on the opposite side).

### Step 4: Substituting Values into the Formula
Substituting the values into the lensmaker's formula:
\[ \frac{1}{f} = (\mu_{air} - 1) \left( \frac{1}{r} - \frac{1}{-r} \right) \]
This simplifies to:
\[ \frac{1}{f} = (1 - 1.33) \left( \frac{1}{r} + \frac{1}{r} \right) \]
\[ \frac{1}{f} = (-0.33) \left( \frac{2}{r} \right) \]
\[ \frac{1}{f} = -\frac{0.66}{r} \]

### Step 5: Analyzing the Focal Length
From the equation:
\[ f = -\frac{r}{0.66} \]
Since the focal length \( f \) is negative, this indicates that the lens behaves like a concave lens.

### Conclusion
A spherical air bubble in water acts as a concave lens.

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