When discussing the properties of concave and convex mirrors, it's essential to understand how we define their focal lengths and radii of curvature. Let's break this down step by step.
Understanding Concave Mirrors
For a concave mirror, the focal point is located in front of the mirror. This means that when light rays parallel to the principal axis hit the mirror, they converge at the focal point. In optics, the convention is to assign a positive value to the focal length of concave mirrors. Therefore, we can say:
- Focal length of concave mirror: Positive
Exploring Convex Mirrors
On the other hand, convex mirrors have a focal point that is virtual and located behind the mirror. When light rays strike a convex mirror, they diverge, and the focal point appears to be behind the mirror. In this case, the focal length is assigned a negative value. Thus, we can conclude:
- Focal length of convex mirror: Negative
Radius of Curvature
The radius of curvature is directly related to the focal length. For mirrors, the radius of curvature is twice the focal length. Therefore, the sign of the radius of curvature follows the same convention as the focal length:
- Radius of curvature for concave mirrors: Positive
- Radius of curvature for convex mirrors: Negative
Final Summary
To summarize:
- For concave mirrors, both the focal length and radius of curvature are positive.
- For convex mirrors, both the focal length and radius of curvature are negative.
Now, looking at the options provided:
- (a) For concave mirror, focal length is taken as positive.
- (b) For convex mirrors, the radius of curvature is taken as negative.
Thus, the correct answer is: (a) a = positive, b = negative.
