📝 Chapter Notes & Revision

Light – Reflection and Refraction

🏫 MP BoardClass 10Science

📐 Formula & Cheat Sheet (English)

Quick Revision Notes & Formula Sheet

Class: 10th Science
Chapter: Light – Reflection and Refraction
Board: MP Board

Introduction to Light

  • Light is a form of energy that produces the sensation of sight in us. It travels in a straight line (rectilinear propagation).
  • Reflection of Light: The bouncing back of light when it strikes a polished, smooth surface like a plane mirror.
  • Refraction of Light: The bending of light when it passes obliquely from one transparent medium to another medium of different optical density.

1. Laws of Reflection

  1. First Law: The incident ray, the reflected ray, and the normal to the mirror at the point of incidence all lie in the same plane.
  2. Second Law: The angle of incidence ($\angle i$) is always equal to the angle of reflection ($\angle r$). $$\angle i = \angle r$$

2. Spherical Mirrors (गोलीय दर्पण)

Spherical mirrors are of two types:

  1. Concave Mirror (अवतल दर्पण): Reflecting surface is curved inwards. (Converging mirror)
  2. Convex Mirror (उत्तल दर्पण): Reflecting surface is curved outwards. (Diverging mirror)

Important Terms:

  • Pole (P): The center of the reflecting surface of a spherical mirror.
  • Center of Curvature (C): The center of the hollow sphere of which the mirror is a part.
  • Radius of Curvature (R): The radius of the hollow sphere of which the mirror is a part.
  • Principal Axis: A straight line passing through the pole and the center of curvature.
  • Principal Focus (F): The point on the principal axis where parallel rays of light actually meet (concave) or appear to diverge from (convex) after reflection.
  • Focal Length ($f$): The distance between the pole (P) and principal focus (F).

Relation between Radius of Curvature and Focal Length:

$$R = 2f \quad \text{or} \quad f = \frac{R}{2}$$

3. Mirror Formula and Magnification

  • Mirror Formula: Relates object distance ($u$), image distance ($v$), and focal length ($f$). $$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$

  • Magnification ($m$): The ratio of the height of the image ($h'$) to the height of the object ($h$). It is also related to $v$ and $u$. $$m = \frac{\text{Height of Image }(h')}{\text{Height of Object }(h)} = -\frac{v}{u}$$

    • If $m$ is negative, the image is real and inverted.
    • If $m$ is positive, the image is virtual and erect.
    • If $|m| = 1$ (Size of image = Size of object), $|m| > 1$ (Magnified), $|m| < 1$ (Diminished).

4. Refraction of Light

Laws of Refraction (Snell's Law):

  1. The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
  2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for the light of a given color and for the given pair of media. $$\frac{\sin i}{\sin r} = \text{constant } (n_{21})$$

Refractive Index ($n$ or $\mu$):

  • Relative Refractive Index ($n_{21}$): Refractive index of medium 2 with respect to medium 1. $$n_{21} = \frac{\text{Speed of light in medium 1 }(v_1)}{\text{Speed of light in medium 2 }(v_2)}$$
  • Absolute Refractive Index ($n_m$): Refractive index of a medium with respect to vacuum or air. $$n = \frac{\text{Speed of light in vacuum }(c)}{\text{Speed of light in medium }(v)}$$ (Note: Speed of light in vacuum, $c = 3 \times 10^8 \text{ m/s}$)

5. Spherical Lenses (गोलीय लेंस)

Lenses are of two types:

  1. Convex Lens (उत्तरा लेंस): Thicker at the middle, thinner at edges. (Converging lens)
  2. Concave Lens (अवตาล लेंस): Thinner at the middle, thicker at edges. (Diverging lens)

Lens Formula:

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Magnification for Lenses ($m$):

$$m = \frac{h'}{h} = \frac{v}{u}$$

6. Power of a Lens (लेंस की क्षमता)

  • Definition: The degree of convergence or divergence of light rays achieved by a lens is expressed as its power. It is defined as the reciprocal of its focal length (in meters).
  • Formula: $$P = \frac{1}{f \text{ (in meters)}}$$ $$P = \frac{100}{f \text{ (in cm)}}$$
  • SI Unit: Dioptre (D).
  • Note:
    • Power of a convex lens is positive (+).
    • Power of a concave lens is negative (-).

7. Sign Convention for Mirrors and Lenses (चि परिपाटी)

  1. All distances are measured from the Pole (P) of the mirror or Optical Center (O) of the lens.
  2. Distances measured in the direction of incident light are taken as positive.
  3. Distances measured opposite to the direction of incident light are taken as negative.
  4. Heights measured upward and perpendicular to the principal axis are positive.
  5. Heights measured downward and perpendicular to the principal axis are negative.

Quick Tip for MP Board Exams: Always write the formula, substitute values with proper signs according to the sign convention, and include SI units in your final answer to score full marks in numericals!