The focal length of spherical mirror is

Options

A. Maximum for red light
B. Maximum for blue light
C. Maximum for white light
D. Same for all lights

Answer

To determine the focal length of a spherical mirror and how it relates to different colors of light, we can follow these steps:

### Step 1: Understand the Definition of Focal Length
The focal length (f) of a spherical mirror is defined as the distance from the mirror's surface to its focus. For a spherical mirror, the focal length is related to the radius of curvature (R) by the formula:
\[ f = \frac{R}{2} \]

### Step 2: Analyze the Dependence on Light Wavelength
The question asks about the focal length of a spherical mirror concerning different colors of light (red, blue, white). It is important to note that the focal length of a spherical mirror does not depend on the wavelength of light. This means that regardless of the color of light incident on the mirror, the focal length remains constant.

### Step 3: Understand the Concept of Achromatic Mirrors
Spherical mirrors are considered achromatic, meaning that their focal length does not change with different wavelengths of light. This is a physical property of the mirror itself and is independent of the light's color.

### Step 4: Consider Reflectivity Variations
While the focal length is constant, the reflectivity of the mirror can vary with different colors of light. Some wavelengths may be reflected better than others, but this does not affect the focal length.

### Conclusion
In conclusion, the focal length of a spherical mirror is the same for all colors of light. Therefore, the answer to the question is that the focal length is the same for red light, blue light, white light, and does not vary with the color of the light.

### Final Answer
The focal length of a spherical mirror is the same for all colors of light.

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