A point object is placed at the center of a glass sphere of radius 6cm and refractive index 1.5. The distance of virtual image from the surface is

Options

A. 6cm
B. 4cm
C. 12cm
D. 9cm

Explanation

To solve the problem of finding the distance of the virtual image from the surface of a glass sphere, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a glass sphere with a radius of 6 cm and a refractive index of 1.5.
- A point object is placed at the center of the sphere.

2. **Identify the Object and Image Locations**:
- The object is located at the center of the sphere, which is at a distance of 0 cm from the center.
- Since the object is at the center, we need to determine where the virtual image will form.

3. **Apply the Refraction Principles**:
- When light rays emanate from the point object at the center, they will strike the inner surface of the sphere.
- Because the object is at the center and the sphere is symmetrical, the light rays will refract at the surface of the sphere.

4. **Determine the Angle of Incidence and Refraction**:
- The angle of incidence for rays striking the surface normally (perpendicular to the surface) is 0 degrees.
- According to Snell's law, if the angle of incidence is 0, the angle of refraction is also 0. Thus, the light rays will continue in a straight line.

5. **Extend the Light Rays**:
- Since the light rays do not converge to form a real image, we extend the refracted rays backward.
- The virtual image will form at the same position as the object, which is at the center of the sphere.

6. **Calculate the Distance from the Surface**:
- The distance from the center of the sphere to the surface is equal to the radius of the sphere.
- Therefore, the distance of the virtual image from the surface of the sphere is equal to the radius of the sphere, which is 6 cm.

### Final Answer:
The distance of the virtual image from the surface of the glass sphere is **6 cm**.

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