To find the focal length of a convex mirror, we use the formula f = R/2, where f is the focal length and R is the radius of curvature. Given that the radius of curvature of the convex mirror is 32 cm, the focal length can be calculated as f = R/2 = 32/2 = 16 cm. Therefore, the focal length of the convex mirror is 16 cm.
Let’s discuss in detail
Understanding the Radius of Curvature
Defining the Mirror’s Curvature: The radius of curvature of a mirror is the radius of the sphere to which the mirror’s surface can be considered a part. For a convex mirror, this radius is measured from the mirror’s surface to the center of the hypothetical sphere.
Formula for Focal Length
Optical Relationship: The focal length of a mirror, particularly a convex mirror, is related to its radius of curvature. This relationship is defined 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 the radius of curvature of the convex mirror as 32 cm, we apply this formula to determine the focal length. By substituting the given value into the formula, we get f = 32/2 = 16 cm.
Result of the Calculation
Determining the Focal Length: The calculation yields a focal length of 16 cm for the convex mirror. This means that the mirror’s focal point, where parallel rays of light appear to diverge from, is 16 cm from the mirror’s surface.
Significance in Practical Applications
Importance in Optical Design: The focal length of a mirror is a crucial factor in its optical properties and applications. In the case of convex mirrors, a 16 cm focal length is significant for applications like vehicle rear-view mirrors, where a wide field of view is essential.