A concave mirror is placed on a horizontal table with its axis directed vertically upward. Let O be the pole of the mirror C its center of curvature and F is the focus. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be

Options

A. real and will remain at C
B. real and located at a point between C and `oo`
C. virtual and located at a point between C and O
D. real and located at a point between C and O

Explanation

To solve the problem, we need to analyze the behavior of light rays when a concave mirror is filled with water. Here’s a step-by-step solution:

### Step 1: Understand the Initial Setup
- A concave mirror is placed with its axis directed vertically upward.
- The pole of the mirror is denoted as O, the center of curvature as C, and the focus as F.
- A point object is placed at C, which means it is at the center of curvature.

**Hint:** Remember that when an object is placed at the center of curvature of a concave mirror, the image formed is real and located at the same point (C).

### Step 2: Determine the Image Formation in Air
- When the object is at C, the rays coming from C reflect off the mirror and converge back at C.
- Thus, the image formed is real and located at C.

**Hint:** Recall the mirror formula and the properties of concave mirrors when the object is at the center of curvature.

### Step 3: Analyze the Effect of Filling the Mirror with Water
- When the mirror is filled with water, the refractive index of the medium changes.
- Light rays traveling from the object at C will now pass from air (rarer medium) into water (denser medium).

**Hint:** Consider how light behaves when it moves from a rarer medium to a denser medium. It bends towards the normal.

### Step 4: Trace the Path of Light Rays
- As the light rays travel from C, they will bend towards the normal when entering the water.
- After reflecting off the mirror, the rays will again exit the water and bend away from the normal as they move from water to air.

**Hint:** Use ray diagrams to visualize how the light rays change direction at the interface of air and water.

### Step 5: Determine the New Image Location
- After tracing the rays, we find that they converge at a point between C and O.
- This indicates that the image formed is real and located between the center of curvature (C) and the pole (O).

**Hint:** Check the characteristics of the image formed by the mirror when the object is at C in a denser medium.

### Conclusion
The image formed when the concave mirror is filled with water is real and located between C and O.

### Final Answer
The correct option is: **Real and located between C and O.**

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