Class 10 Science | Mirror Formula Derivation | Concave & Convex Mirror | Light Reflection

In this video, we will cover Class 10 Science Chapter 1: Light Reflection and Refraction in detail. You will learn about mirror formula derivation, concave mirror, convex mirror, image formation by concave mirror, and the mirror formula for both concave and convex mirrors step by step. This video is specially designed for CBSE Class 10 students to understand the topic with clarity and score high marks in exams. --- 🔹 Introduction to Light (Class 10 Science Chapter 1) Light is a form of energy that enables us to see objects around us. The study of reflection of light and refraction of light is an important part of Class 10 Science Chapter 1. In this lesson, we focus on how mirrors form images and how the mirror formula is derived using simple geometry. --- 🔹 Reflection of Light Reflection is the phenomenon in which light rays strike a polished surface (like a mirror) and bounce back into the same medium. Laws of Reflection: 1. The angle of incidence = angle of reflection. 2. The incident ray, reflected ray, and normal to the surface all lie in the same plane. --- 🔹 Types of Spherical Mirrors 1. Concave Mirror (Converging Mirror): A concave mirror is spherical with the reflecting surface curved inward. It forms real or virtual images depending on the object’s position. 2. Convex Mirror (Diverging Mirror): A convex mirror has its reflecting surface curved outward. It always forms virtual, erect, and diminished images. --- 🔹 Image Formation by Concave Mirror The image formed by a concave mirror depends on the position of the object: At infinity → highly diminished, real, and inverted at the focus. Beyond the center of curvature → real, inverted, smaller between C and F. At the center of curvature (C) → real, inverted, same size at C. Between C and F → real, inverted, magnified beyond C. At the focus (F) → image at infinity. Between F and pole → virtual, erect, magnified behind the mirror. --- 🔹 Mirror Formula The mirror formula establishes a relationship between: Object distance (u), Image distance (v), and Focal length (f). The formula is: \frac{1}{f} = \frac{1}{v} + \frac{1}{u} Where: f = focal length of the mirror u = object distance (always taken negative for real objects in mirror formula convention) v = image distance --- 🔹 Derivation of Mirror Formula (Step by Step) Let us derive the mirror formula for a concave mirror: 1. Consider a concave mirror with pole (P), center of curvature (C), and principal axis. 2. An object AB is placed beyond the center of curvature. 3. A ray from point A passes parallel to the principal axis and after reflection passes through focus F. 4. Another ray passes through the center of curvature C and reflects back on the same path. 5. The two reflected rays meet at point A′, forming image A′B′. From the geometry: Using similar triangles: \frac{AB}{A'B'} = \frac{PB}{P'B'} = \frac{u}{v} Using another pair of similar triangles: \frac{AB}{A'B'} = \frac{PC}{PF} = \frac{u}{f} By equating both ratios: \frac{u}{v} = \frac{u}{f} Rearranging: \frac{1}{f} = \frac{1}{v} + \frac{1}{u} Thus, the mirror formula is derived. 👉 The same formula applies to convex mirrors with proper sign convention. --- 🔹 Mirror Formula for Concave Mirror For a concave mirror, the focal length (f) is taken as negative, and object distance (u) is also negative for real objects. By substituting correct signs, you can easily calculate the position of the image. --- 🔹 Mirror Formula for Convex Mirror For a convex mirror, the focal length (f) is positive, object distance (u) is negative (for real objects), and the image distance (v) is always positive as images are formed behind the mirror. --- 🔹 Applications of Concave and Convex Mirrors Concave Mirror Uses: In torches, headlights, solar cookers, shaving mirrors, and telescopes. Convex Mirror Uses: In rear-view mirrors of vehicles, surveillance mirrors, and ATM security mirrors. --- 🔹 Why is Mirror Formula Important for Class 10? It is a most expected exam question in CBSE, ICSE, and State Boards. It helps in solving numericals in reflection and refraction. It forms the base for higher-level optics in Class 11 & 12 Physics. #Class10Science #MirrorFormulaDerivation #LightReflectionRefraction #ConcaveMirror #ConvexMirro