Light: Reflection & Refraction

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### Introduction to Light - Light is a form of energy that enables us to see. - It travels in straight lines (rectilinear propagation). - **Dual Nature:** Light exhibits both wave-like and particle-like properties. - **Wave Nature:** Explains interference, diffraction. - **Particle Nature (Photons):** Explains photoelectric effect. - **Speed of Light (c):** Approximately $3 \times 10^8$ m/s in vacuum. ### Reflection of Light: Laws & Terms - **Reflection:** The bouncing back of light when it strikes a surface. - **Types of Reflection:** - **Specular (Regular):** From smooth surfaces (mirrors), parallel rays remain parallel. - **Diffuse (Irregular):** From rough surfaces, parallel rays scatter in different directions. - **Key Terms:** - **Incident Ray:** The ray of light falling on the surface. - **Reflected Ray:** The ray of light sent back by the surface. - **Normal:** An imaginary line perpendicular to the surface at the point of incidence. - **Angle of Incidence ($i$):** Angle between incident ray and normal. - **Angle of Reflection ($r$):** Angle between reflected ray and normal. - **Laws of Reflection:** 1. The angle of incidence is equal to the angle of reflection ($i = r$). 2. The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane. ### Plane Mirrors - **Image Formation:** - Always **virtual** (cannot be obtained on a screen). - Always **erect** (upright). - **Laterally inverted** (left appears right and vice versa). - **Same size** as the object. - **Same distance** behind the mirror as the object is in front. - **Uses:** Dressing mirrors, periscopes, kaleidoscopes. ### Spherical Mirrors: Concave & Convex - **Definition:** Mirrors that are part of a hollow sphere. - **Key Terms:** - **Pole (P):** Center of the reflecting surface. - **Centre of Curvature (C):** Center of the sphere from which the mirror is cut. - **Radius of Curvature (R):** Distance PC. - **Principal Axis:** Line joining P and C. - **Principal Focus (F):** Point on principal axis where parallel rays converge (concave) or appear to diverge from (convex) after reflection. - **Focal Length (f):** Distance PF. $f = R/2$. - **Aperture:** The diameter of the reflecting surface. #### Concave Mirror (Converging Mirror) - Reflecting surface is curved inwards. - **Ray Diagrams (Rules):** 1. Ray parallel to principal axis passes through F after reflection. 2. Ray passing through F becomes parallel to principal axis after reflection. 3. Ray passing through C reflects back along the same path. 4. Ray incident obliquely at P reflects obliquely, making equal angles with principal axis. - **Image Formation by Concave Mirror:** | Object Position | Image Position | Nature of Image | Size of Image | |---------------------------|----------------------------|-----------------|-------------------| | At infinity | At F | Real, Inverted | Highly diminished | | Beyond C | Between F and C | Real, Inverted | Diminished | | At C | At C | Real, Inverted | Same size | | Between C and F | Beyond C | Real, Inverted | Enlarged | | At F | At infinity | Real, Inverted | Highly enlarged | | Between F and P | Behind the mirror | Virtual, Erect | Enlarged | - **Uses:** Shaving mirrors, dentists' mirrors, headlights, solar furnaces. #### Convex Mirror (Diverging Mirror) - Reflecting surface is curved outwards. - **Ray Diagrams (Rules):** 1. Ray parallel to principal axis appears to diverge from F after reflection. 2. Ray directed towards F becomes parallel to principal axis after reflection. 3. Ray directed towards C reflects back along the same path. 4. Ray incident obliquely at P reflects obliquely, making equal angles. - **Image Formation by Convex Mirror:** - Always forms **virtual, erect, and diminished** images. - Image is always formed **behind the mirror, between P and F**. - **Uses:** Rear-view mirrors in vehicles, shop security mirrors. ### New Cartesian Sign Convention - **Origin:** Pole (P) of the mirror/lens. - **Principal Axis:** X-axis. - **Distances:** - Measured from P. - Distances to the right of P are positive. - Distances to the left of P are negative. - **Heights:** - Measured perpendicular to principal axis. - Upward heights (above axis) are positive. - Downward heights (below axis) are negative. - **Focal Length (f):** - Concave mirror: negative - Convex mirror: positive ### Mirror Formula & Magnification - **Mirror Formula:** $$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$ - $u$: object distance (always negative for real objects) - $v$: image distance - $f$: focal length - **Magnification (m):** Ratio of image height to object height. $$m = \frac{h'}{h} = -\frac{v}{u}$$ - $h'$: height of image - $h$: height of object - **Interpreting m:** - $|m| > 1$: Enlarged image - $|m| = 1$: Same size image - $|m| 0$: Virtual and erect image - $m ### Refraction of Light: Laws & Terms - **Refraction:** The bending of light as it passes from one transparent medium to another. - **Cause:** Change in speed of light as it enters a different medium. - **Key Terms:** - **Incident Ray:** Ray falling on the interface. - **Refracted Ray:** Ray that enters the second medium. - **Angle of Incidence ($i$):** Angle between incident ray and normal. - **Angle of Refraction ($r$):** Angle between refracted ray and normal. - **Laws of Refraction:** 1. The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane. 2. **Snell's Law:** The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media and for a given colour of light. $$\frac{\sin i}{\sin r} = \text{constant} = n_{21}$$ - $n_{21}$ is the **refractive index** of medium 2 with respect to medium 1. ### Refractive Index (n) - **Absolute Refractive Index ($n_m$):** Ratio of speed of light in vacuum (c) to speed of light in the medium (v). $$n_m = \frac{c}{v}$$ - **Relative Refractive Index ($n_{21}$):** Ratio of speed of light in medium 1 ($v_1$) to speed of light in medium 2 ($v_2$). $$n_{21} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$$ - If $n_2 > n_1$, medium 2 is optically denser than medium 1. - If light goes from rarer to denser medium (e.g., air to glass), it bends **towards the normal** ($r i$). - **Optical Density:** A measure of how much a medium slows down light. Denser medium = higher refractive index. ### Refraction Through a Rectangular Glass Slab - Light bends towards the normal upon entering the glass (rarer to denser). - Light bends away from the normal upon exiting the glass (denser to rarer). - The emergent ray is parallel to the incident ray, but laterally displaced. ### Lenses: Convex & Concave - **Definition:** Transparent materials bounded by two spherical surfaces or one spherical and one plane surface. - **Key Terms:** - **Optical Centre (O):** Central point of the lens. - **Principal Axis:** Line passing through O and centres of curvature. - **Principal Focus (F1, F2):** Points on principal axis where parallel rays converge (convex) or appear to diverge from (concave). Each lens has two focal points. - **Focal Length (f):** Distance OF. #### Convex Lens (Converging Lens) - Thicker in the middle, thinner at the edges. - **Ray Diagrams (Rules):** 1. Ray parallel to principal axis passes through F2 after refraction. 2. Ray passing through F1 becomes parallel to principal axis after refraction. 3. Ray passing through O goes undeviated. - **Image Formation by Convex Lens:** | Object Position | Image Position | Nature of Image | Size of Image | |---------------------------|----------------------------|-----------------|-------------------| | At infinity | At F2 | Real, Inverted | Highly diminished | | Beyond 2F1 | Between F2 and 2F2 | Real, Inverted | Diminished | | At 2F1 | At 2F2 | Real, Inverted | Same size | | Between F1 and 2F1 | Beyond 2F2 | Real, Inverted | Enlarged | | At F1 | At infinity | Real, Inverted | Highly enlarged | | Between F1 and O | On the same side as object | Virtual, Erect | Enlarged | - **Uses:** Magnifying glass, cameras, telescopes, spectacles for hypermetropia. #### Concave Lens (Diverging Lens) - Thinner in the middle, thicker at the edges. - **Ray Diagrams (Rules):** 1. Ray parallel to principal axis appears to diverge from F1 after refraction. 2. Ray directed towards F2 becomes parallel to principal axis after refraction. 3. Ray passing through O goes undeviated. - **Image Formation by Concave Lens:** - Always forms **virtual, erect, and diminished** images. - Image is always formed **between O and F1** on the same side as the object. - **Uses:** Spectacles for myopia, Galilean telescopes. ### Lens Formula & Magnification - **New Cartesian Sign Convention (for lenses):** Similar to mirrors, but focal length of convex lens is positive, concave lens is negative. - **Lens Formula:** $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$ - $u$: object distance - $v$: image distance - $f$: focal length - **Magnification (m):** $$m = \frac{h'}{h} = \frac{v}{u}$$ - $h'$: height of image - $h$: height of object - **Interpreting m:** Same as for mirrors regarding size and nature (positive for virtual/erect, negative for real/inverted). ### Power of a Lens (P) - **Definition:** The degree of convergence or divergence of light rays achieved by a lens. - **Formula:** $$P = \frac{1}{f}$$ (where f is in meters) - **Unit:** Dioptre (D). 1 D = $1 \text{ m}^{-1}$. - **Sign Convention:** - Convex lens (converging): $f$ is positive, so $P$ is positive. - Concave lens (diverging): $f$ is negative, so $P$ is negative. - **Combination of Lenses:** For lenses in contact, $P_{total} = P_1 + P_2 + P_3 + ...$