State the direction of incident ray which after reflection from a spherical mirror retraces its path. Give a reason to your answer.

Answer

To solve the question, we need to determine the direction of the incident ray that, after reflecting from a spherical mirror, retraces its path. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Reflection
When light rays strike a mirror, they reflect off the surface. The angle at which the light ray hits the mirror (angle of incidence) is equal to the angle at which it reflects off the mirror (angle of reflection).

**Hint:** Remember that the law of reflection states that the angle of incidence is equal to the angle of reflection.

### Step 2: Identify the Spherical Mirror
A spherical mirror can either be concave or convex. For this problem, we will consider a concave mirror, which is commonly used in optics.

**Hint:** Think about the properties of concave mirrors and how they focus light.

### Step 3: Locate the Center of Curvature
The center of curvature (C) is a point that is located at a distance equal to the radius of the sphere from the mirror's surface. When a ray of light is directed towards this point, it behaves in a specific way.

**Hint:** Recall that the center of curvature is crucial in determining how light interacts with the mirror.

### Step 4: Analyze the Incident Ray from the Center of Curvature
When a light ray is incident from the center of curvature (C) of the spherical mirror, it strikes the mirror perpendicularly. This means that the angle of incidence (I) is 0 degrees.

**Hint:** Visualize the situation: if the ray comes from the center of curvature, it hits the mirror straight on.

### Step 5: Apply the Law of Reflection
Since the angle of incidence is 0 degrees, the angle of reflection (R) will also be 0 degrees. This means that the ray will reflect back along the same path it came from.

**Hint:** Remember that when the angle of incidence is zero, the light ray will not change direction.

### Step 6: Conclusion
Thus, the direction of the incident ray that retraces its path after reflection from a spherical mirror is towards the center of curvature.

**Final Answer:** The incident ray must be directed towards the center of curvature of the spherical mirror in order to retrace its path.

---