Reflection of light by curved surfaces for class 10th

Reflection of light by curved surfaces, particularly mirrors, is an important concept in optics. For Class 10 NCERT, it’s essential to understand how light interacts with concave and convex mirrors. Here’s a detailed explanation:

Curved Mirrors

Curved mirrors can be of two types:

1. Concave Mirrors: These mirrors curve inward like the inside of a bowl.
2. Convex Mirrors: These mirrors curve outward like the outside of a sphere.

Basic Terms

1. Pole (P): The center of the mirror’s surface.
2. Center of Curvature (C): The center of the sphere from which the mirror is a part. For a concave mirror, this point lies in front of the mirror, and for a convex mirror, it lies behind the mirror.
3. Radius of Curvature (R): The distance between the pole and the center of curvature.
4. Principal Axis: The straight line passing through the pole and the center of curvature.
5. Focus (F): The point where parallel rays of light either converge (concave) or appear to diverge from (convex) after reflection.
6. Focal Length (f): The distance between the pole and the focus. It is half of the radius of curvature (f = R/2).

Reflection in Concave Mirrors

For concave mirrors, the behavior of reflected rays depends on the position of the object relative to the focus (F) and the center of curvature (C).

1. Object at Infinity: The rays coming from infinity are parallel to the principal axis. After reflection, these rays converge at the focus.
   • Image: Formed at the focus (F), real, inverted, and highly diminished.
2. Object Beyond C: The rays reflect and meet between the focus (F) and the center of curvature (C).
   • Image: Between F and C, real, inverted, and diminished.
3. Object at C: The rays reflect and meet at the center of curvature (C).
   • Image: At C, real, inverted, and of the same size.
4. Object Between C and F: The rays reflect and meet beyond the center of curvature (C).
   • Image: Beyond C, real, inverted, and magnified.
5. Object at F: The rays reflect and become parallel to the principal axis.
   • Image: At infinity, real, inverted, and highly magnified.
6. Object Between F and P: The rays diverge after reflection, but when extended backward, they appear to come from a point behind the mirror.
   • Image: Behind the mirror, virtual, erect, and magnified.

Reflection in Convex Mirrors

Convex mirrors always form virtual, erect, and diminished images regardless of the position of the object. The rays diverge after reflection, and when extended backward, they appear to come from a point behind the mirror (the virtual focus).

1. Object at Infinity: The rays appear to diverge from the focus (F) behind the mirror.
   • Image: At the focus (F), virtual, erect, and highly diminished.
2. Object at Finite Distance: The rays appear to diverge from a point between the focus (F) and the pole (P) behind the mirror.
   • Image: Between F and P, virtual, erect, and diminished.

Ray Diagrams

Ray diagrams help in understanding image formation by curved mirrors. Here are key rays to consider for both concave and convex mirrors:

1. A ray parallel to the principal axis: Reflects through the focus (F) for concave mirrors and appears to diverge from the focus (F) for convex mirrors.
2. A ray passing through the center of curvature (C): Reflects back along the same path.
3. A ray passing through (or directed towards) the focus (F): Reflects parallel to the principal axis.
4. A ray incident at the pole (P): Reflects symmetrically about the principal axis.

Understanding these concepts will help you solve problems related to image formation by curved mirrors and grasp the fundamentals of reflection in optics.