A solid, transparent sphere has a small, opaque dot at its center. When observed from outside, the apparent position of the dot will be

Options

A. Closer to the eye than its actual position
B. Farther away from the eye than its actual position
C. The same as its acutal position
D. Independent of the refractive index of the sphere

Answer

To solve the problem of determining the apparent position of a small opaque dot located at the center of a solid transparent sphere when observed from outside, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a solid transparent sphere with a small opaque dot at its center.
- The dot is opaque, meaning it does not emit or transmit light, but it is surrounded by a medium (the transparent sphere) that can refract light.

2. **Light Rays from the Dot**:
- When light rays emanate from the dot at the center, they travel in all directions.
- As these rays reach the surface of the sphere, they will interact with the spherical surface.

3. **Normal Incidence**:
- At the center of the sphere, the light rays are effectively hitting the surface at normal incidence (perpendicular to the surface).
- According to the laws of refraction, when light strikes a surface at normal incidence, it does not bend or change direction.

4. **Apparent Position of the Dot**:
- Since the rays do not deviate due to normal incidence, the observer outside the sphere will see the rays as if they are coming straight from the dot at the center.
- Therefore, the apparent position of the dot will be the same as its actual position, which is at the center of the sphere.

5. **Conclusion**:
- The apparent position of the dot, when viewed from outside the transparent sphere, will be at the center of the sphere itself.

### Final Answer:
The apparent position of the dot will be at the center of the sphere.

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