There is a solid transparent sphere with a point object embedded at its centre. Apparent location of the point object will be

Options

A. closer to eye than its actual location
B. farther away from eye than its actual location
C. same as its actual location
D. same for any material

Explanation

To determine the apparent location of a point object embedded at the center of a solid transparent sphere, we can analyze the situation using the principles of optics. Here’s a step-by-step solution:

### Step 1: Understand the setup
We have a solid transparent sphere with a point object located at its center. The radius of the sphere is denoted as \( R \).

**Hint:** Visualize the sphere and the point object at its center to understand the light path.

### Step 2: Analyze light rays
When light rays emanate from the point object at the center, they travel in all directions. However, since the object is at the center of a symmetric medium (the sphere), the light rays will behave uniformly.

**Hint:** Consider how light travels through a medium and how it behaves at the boundaries.

### Step 3: Normal incidence
Any light ray that travels directly outward from the center will strike the surface of the sphere perpendicularly (normal incidence). At normal incidence, there is no refraction; the light continues in the same direction.

**Hint:** Recall the principle that light does not bend when it strikes a surface at a 90-degree angle.

### Step 4: Apparent location of the object
Since the point object is at the center and light rays travel outward without deviation, the apparent position of the object, as viewed from outside the sphere, remains the same as its actual position.

**Hint:** Think about how the position of the object appears to an observer outside the sphere.

### Step 5: Conclusion
The apparent location of the point object embedded at the center of the solid transparent sphere is the same as its actual position. This conclusion holds true regardless of the material of the sphere, as there is no refraction occurring at normal incidence.

**Hint:** Consider the implications of this conclusion for different materials and how it relates to the concept of optical density.

### Final Answer
The apparent location of the point object will be the same as its actual position.