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

Options

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

Answer

To determine 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 1: Understand the Setup
We have a solid transparent sphere with a small opaque dot at its center. The observer is looking at the sphere from outside.

### Step 2: Identify the Light Rays
When light rays travel from the opaque dot, they will pass through the transparent material of the sphere. We need to consider how these rays behave as they encounter the sphere's surface.

### Step 3: Apply the Law of Refraction
According to the law of refraction (Snell's Law), when light passes from one medium to another, it bends. However, if the light ray strikes the surface of the sphere at the normal (perpendicular), it will not bend. This is known as normal incidence.

### Step 4: Analyze the Path of Light Rays
Since the dot is at the center of the sphere, light rays emitted from the dot will strike the surface of the sphere at the normal. Therefore, these rays will continue in a straight line without bending.

### Step 5: Determine the Apparent Position
Because the light rays do not bend when they exit the sphere, the observer will see the dot at its actual position, which is at the center of the sphere.

### Step 6: Conclusion
The apparent position of the opaque dot, when viewed from outside the sphere, will be at the same position as its actual position.

### Final Answer
The apparent position of the dot will be at the same position as its actual position.

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