Detailed Notes from Toppers: Refraction at Spherical Surfaces

---

Reference: NCERT Physics, 11th and 12th Standards

---

1. Spherical Refracting Surfaces

- Introduction: Surfaces separating two media with different refractive indices, causing light to change direction. - Convex vs. Concave Lenses: Lenses with curved surfaces facing away or toward the incident light, respectively. - Types of Lenses: Converging (convex) and diverging (concave) lenses.

---

2. Laws of Refraction

- Snell's Law: $\frac{\sin i}{\sin r}=\frac{n_2}{n_1}$, where i is the angle of incidence, r is the angle of refraction, and $n_1$ and $n_2$ are the refractive indices of the first and second media, respectively. - Refractive Index: Measure of how much light bends when passing from one medium to another.

---

3. Focal Length and Image Formation

- Focal Point: Point where parallel light rays converge or appear to diverge after passing through a lens. - Principal Axis: Line passing through the optical center of the lens and perpendicular to the lens surfaces. - Focal Length (f): Distance between the lens and its focal point.

---

4. Thin Lens Equations

- Lens Equation (Equation of Linear Magnification): $\frac{1}{f}=\frac{1}{d_0}+\frac{1}{d_i}$, where $d_0$ and $d_i$ are object and image distances, respectively. - Magnification Equation: $m=\frac{h_i}{h_0}=\frac{-d_i}{d_0}$, where $h_0$ and $h_i$ are object and image heights, respectively.

---

5. Ray Diagrams

- Drawing Conventions: Light rays from an object parallel to the principal axis pass through the focal point after refraction, while rays passing through the optical center continue straight. - Image Location and Characteristics: Use constructed diagrams to determine image location and features.

---

6. Sign Conventions

- Distance Conventions: Positive (negative) values indicate distances measured in the same (opposite) direction as the incident light. - Focal Length Convention: Positive (negative) focal length for converging (diverging) lenses.

---

7. Image Characteristics

- Virtual Image: Cannot be projected onto a screen, appears to be located behind the mirror (diverging lenses). - Real Image: Can be projected onto a screen, appearing on the opposite side of the lens to the object (converging lenses). - Upright vs. Inverted Image: Image orientation depends on object position and lens type.

---

8. Special Cases

- Parallel Rays: Rays parallel to the principal axis converge (convex lens) or appear to diverge (concave lens) at the focal point. - Principal Rays: Two rays used in ray diagrams, one parallel and one passing through the optical center of the lens.

---

9. Lens Combinations

- Equivalent Focal Length: Total effect of multiple lenses is equivalent to a single lens with a focal length $f_e$, where $\frac{1}{f_e}=\sum _{i=1}^n\frac{1}{f_i}$, where $f_i$ is the focal length of each lens. - Final Image Characteristics: Determined using equivalent focal length and combined lens equation.

---

10. Applications

- Microscope: Enlarges small objects for observation. - Telescope: Magnifies distant objects. - Camera: Forms real, inverted images on photosensitive surfaces.

---

11. Chromatic and Spherical Aberrations

- Chromatic Aberration: Variation of focal length with wavelength, causing different colors of light to focus at different points. - Spherical Aberration: Imperfection in the focusing of light rays due to the spherical shape of the lens, leading to distorted images.