For a spherical mirror, the relationship between the radius of curvature (R) and the focal length (f) is given by the formula f= R/2. If the radius of curvature of a spherical mirror is 20 cm, its focal length can be calculated as f = 20/2 =10 cm.

Therefore, the focal length of the spherical mirror is 10 cm. This relationship holds true for both concave and convex mirrors.

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## Understanding the Radius of Curvature

*Basic Concept*: The radius of curvature of a spherical mirror refers to the radius of the imaginary sphere of which the mirror’s surface forms a part. It is a key parameter in defining the mirror’s curvature and optical properties.

### Relationship between Radius of Curvature and Focal Length

*Fundamental Optical Principle*: The focal length of a spherical mirror is directly related to its radius of curvature. This relationship is expressed by the formula f = R/2, where f is the focal length and R is the radius of curvature.

#### Calculation of Focal Length

*Applying the Formula*: Given a spherical mirror with a radius of curvature of 20 cm, we apply the formula to find the focal length. By substituting R=20 cm into the formula f = R/2, we get f =20/2 = 10 cm

##### Result of the Calculation

*Determining Focal Length*: From the calculation, the focal length of the mirror is found to be 10 cm. This means that parallel rays of light, after reflecting off the mirror, will converge or appear to diverge from a point 10 cm from the mirror’s surface.

###### Implications in Optical Design

*Significance in Optics*: The focal length is crucial in designing optical systems, as it determines how the mirror will focus light. A 10 cm focal length is a common specification in various optical applications, including telescopes, cameras, and other imaging devices.

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