There is a small black dot at the centre C of a solid glass sphere of refractive index `mu`. When seen from outside, the dot will appear to be located

Options

A. Away from the C for all values of mu
B. At C for all values of mu.
C. At C for `mu=1.5,` but away from C for mu not equal to `1.5`
D. At `C` for `2ltmult1.5`

Explanation

To solve the problem of where the small black dot at the center of a solid glass sphere appears when viewed from outside, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a solid glass sphere with a refractive index \( \mu \).
- A small black dot is located at the center \( C \) of the sphere.

2. **Light Rays Emission**:
- When light rays emanate from the black dot at the center, they radiate outward in all directions.

3. **Refraction at the Surface**:
- As these light rays reach the surface of the glass sphere, they will undergo refraction. However, since the dot is at the center, the rays that are emitted towards the surface are perpendicular to the surface at the point of incidence.

4. **Normal to the Surface**:
- At the point where the rays hit the surface, the normal (a line perpendicular to the surface) is aligned with the direction of the rays coming from the center. Therefore, the angle of incidence is \( 0^\circ \).

5. **Applying Snell's Law**:
- According to Snell's law, \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \).
- Here, \( n_1 \) is the refractive index of air (approximately 1), and \( n_2 \) is the refractive index of glass (\( \mu \)).
- Since the angle of incidence \( \theta_1 = 0^\circ \), the sine of \( 0^\circ \) is \( 0 \). Thus, the light rays will pass straight through without any deviation.

6. **Conclusion**:
- Since the rays pass straight through the surface without bending, the black dot will appear to be located at the center \( C \) of the sphere when viewed from outside.
- Therefore, regardless of the refractive index \( \mu \), the dot will always appear at the center.

### Final Answer:
The dot will appear to be located at the center of the sphere.

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