The sum of the reciprocals of object distance and image distance is equal to the ___________ of a mirror.

Options

A. focal length
B. reciprocal of the focal length
C. radius of curvature
D. reciprocal of the radius of curvature

Explanation

To solve the question, "The sum of the reciprocals of object distance and image distance is equal to the ___________ of a mirror," we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mirror Formula**: The mirror formula relates the object distance (U), image distance (V), and focal length (F) of a mirror. It is given by:
\[ \frac{1}{F} = \frac{1}{U} + \frac{1}{V} \]

2. **Identify the Reciprocals**: According to the question, we need to find the sum of the reciprocals of the object distance and the image distance. This can be expressed as:
\[ \frac{1}{U} + \frac{1}{V} \]

3. **Relate to Focal Length**: From the mirror formula, we can see that:
\[ \frac{1}{U} + \frac{1}{V} = \frac{1}{F} \]
This shows that the sum of the reciprocals of the object distance and image distance is equal to the reciprocal of the focal length.

4. **Conclude the Answer**: Therefore, the sum of the reciprocals of the object distance and image distance is equal to the reciprocal of the focal length of the mirror.

### Final Answer:
The sum of the reciprocals of object distance and image distance is equal to the **reciprocal of the focal length** of a mirror.

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