A ray of light falls on the surface of a spherical glass paper weight making an angle `alpha` with the normal and is refracted in the medium at an angle `beta`. The angle of deviation of the emergent ray from the direction of the incident ray is :

Options

A. `(alpha-beta)`
B. `2(alpha-beta)`
C. `(alpha-beta)//2`
D. `(beta-alpha)`

Answer

To solve the problem of finding the angle of deviation of the emergent ray from the direction of the incident ray when a ray of light passes through a spherical glass paperweight, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Incident Ray and Angles**:
- Let the incident ray make an angle \( \alpha \) with the normal at the first surface of the spherical paperweight.
- The ray is refracted into the glass at an angle \( \beta \).

2. **Determine the Deviation at the First Surface**:
- The deviation caused by the first refraction can be calculated as:
\[ \text{Deviation}_1 = \alpha - \beta \]

3. **Consider the Emergence from the Second Surface**:
- When the ray reaches the second surface of the glass (the surface where it exits), it will again refract.
- At this surface, the angle of incidence will be \( \beta \) (the angle at which the ray enters the air from the glass).
- The angle of emergence will be \( \alpha \) (the angle the ray makes with the normal as it exits).

4. **Determine the Deviation at the Second Surface**:
- The deviation caused by the second refraction can be calculated as:
\[ \text{Deviation}_2 = \beta - \alpha \]

5. **Calculate the Total Deviation**:
- The total deviation of the emergent ray from the direction of the incident ray is the sum of the deviations at both surfaces:
\[ \text{Total Deviation} = \text{Deviation}_1 + \text{Deviation}_2 \]
- Substituting the values:
\[ \text{Total Deviation} = (\alpha - \beta) + (\beta - \alpha) = 2(\alpha - \beta) \]

6. **Final Result**:
- Thus, the angle of deviation of the emergent ray from the direction of the incident ray is:
\[ \text{Total Deviation} = 2(\alpha - \beta) \]

### Conclusion:
The angle of deviation of the emergent ray from the direction of the incident ray is \( 2(\alpha - \beta) \).