If an object is placed at the centre of a glass sphere and it is seen from outside, then prove that its virtual image is also formed at centre.

Explanation

To prove that the virtual image of an object placed at the center of a glass sphere is also formed at the center, we can follow these steps:

### Step 1: Understand the Setup
- Consider a glass sphere with a center point O. An object is placed exactly at this center point O.

### Step 2: Ray Diagram
- When light rays emanate from the object at point O, they travel in all directions. Since the object is at the center, these rays will strike the inner surface of the glass sphere.

### Step 3: Normal to the Surface
- At the point where each ray strikes the inner surface of the sphere, we can draw a normal line (a line perpendicular to the surface) at that point. Since the object is at the center, each ray will strike the surface at a point where the normal is directed outward from the center.

### Step 4: Refraction of Light
- According to the laws of refraction, when light travels from a denser medium (glass) to a less dense medium (air), it bends away from the normal. Therefore, the rays that strike the surface of the glass sphere will bend away from the normal.

### Step 5: Direction of Emergence
- As the rays emerge from the glass sphere, they will continue to travel in straight lines. Since they are emanating from the center and bending away from the normal, they will appear to diverge from the center point O.

### Step 6: Virtual Image Formation
- The diverging rays, when extended backward, will appear to converge at point O. This means that an observer looking from outside the sphere will perceive a virtual image of the object at the center O.

### Conclusion
- Therefore, we conclude that the virtual image of the object placed at the center of the glass sphere is also formed at the center.

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