2. OPTICS

 Welcome to Rajasthan Polytechnic Physics (2002) Notes for 2nd Semester Students!

Hello, Polytechnic students! 🎓
Struggling with Physics for your 2nd semester? Don’t worry, I’ve got you covered! Here are detailed handwritten notes on essential Physics topics for your 2nd-semester exams. These notes are simplified and cover key concepts with examples to make studying easier and effective.

Download Your Notes

Additionally, you can join our WhatsApp and Telegram groups for easy access to PDF and Handwritten Notes as well as updates on new materials.

We hope this blog helps you in your academic journey.

📢 🔔 Important:
👉 Full PDF available in our WhatsApp Group | Telegram Channel
👉 Watch the full lecture on YouTube: BTER Polytechnic Classes

• Access Chapter-wise Video Tutorials:
  • Physics Complete Playlist - Watch Now

2. OPTICS

Optics is the study of light and its behavior, including reflection, refraction, and how light interacts with different materials. It’s a crucial part of physics because it helps explain how we see the world around us, how lenses work, and how optical devices are designed.

---

2.1 Basic Optical Laws

2.1.1 Reflection and Refraction

Reflection:

• Reflection occurs when light bounces off a surface. It follows two main laws:

  1. Angle of incidence (i) is equal to the angle of reflection (r).
  2. The incident ray, reflected ray, and normal (perpendicular to the surface) all lie in the same plane.

  Formula: $i=r$

  Example: If a light ray hits a mirror at 30°, the angle of reflection will also be 30°.

Refraction:

• Refraction is the bending of light as it passes from one medium to another (like from air to water or from air to glass).

  • Snell’s Law gives the relationship between the angles and refractive indices of the two media:
  $$\frac{\sin i}{\sin r} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$$

  Where:

  • $i$ = Angle of incidence
  • $r$ = Angle of refraction
  • $v_1, v_2$ = Speeds of light in the two media
  • $n_1, n_2$ = Refractive indices of the two media

Refractive Index (n):
It is the ratio of the speed of light in vacuum ($c$) to the speed of light in a medium ($v$):

$$n = \frac{c}{v}$$

For example, the refractive index of water is approximately 1.33, meaning light travels slower in water than in a vacuum.

---

2.1.2 Lens Formula and Power of a Lens (Only Formula)

Lens Formula:
The lens formula relates the focal length (f), object distance (u), and image distance (v) for a lens. It is:

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

Where:

• $f$ = Focal length of the lens
• $v$ = Image distance from the lens (positive for real images, negative for virtual images)
• $u$ = Object distance from the lens (always negative in the case of real objects for lenses)

Power of a Lens (P):
The power of a lens is the reciprocal of its focal length (in meters):

$$P = \frac{1}{f}$$

The unit of power is diopters (D). A lens with a focal length of 1 meter has a power of 1 diopter.

---

2.2 Total Internal Reflection

2.2.1 Critical Angle and Conditions for Total Internal Reflection

Total Internal Reflection:
This phenomenon occurs when a light ray strikes the boundary of a denser medium (like glass or water) at an angle greater than the critical angle. In this case, the light is completely reflected back into the denser medium instead of refracting into the less dense medium.

Critical Angle:
The critical angle (θ_c) is the angle of incidence at which the angle of refraction is 90° (i.e., the refracted ray travels along the boundary). This is given by the formula:

$$\sin \theta_c = \frac{n_2}{n_1}$$

Where:

• $n_1$ = refractive index of the denser medium
• $n_2$ = refractive index of the rarer medium

For example, for light traveling from water ($n_1 = 1.33$) to air ($n_2 = 1.00$):

$$\sin \theta_c = \frac{1.00}{1.33} = 0.75 \quad \Rightarrow \quad \theta_c = \sin^{-1}(0.75) \approx 48.6^\circ$$

This means that if the angle of incidence is greater than 48.6°, total internal reflection will occur.

Conditions for Total Internal Reflection:

1. Light must travel from a denser medium to a rarer medium (e.g., from water to air).
2. The angle of incidence must exceed the critical angle.

---

2.2.2 Applications of Total Internal Reflection in Optical Fibers

Optical Fibers:
Optical fibers use the principle of total internal reflection to transmit light signals over long distances. In these fibers:

• The core of the fiber has a higher refractive index than the cladding.
• Light signals are sent through the core and are repeatedly reflected along the length of the fiber without loss of signal.

Applications:

• Telecommunications: Optical fibers are used to transmit data for telephones and the internet.
• Endoscopy: In medical procedures, optical fibers are used in endoscopes for viewing inside the body.
• Light Guides: Used in various optical instruments and systems for transmitting light.

---

2.3 Optical Instruments

2.3.1 Simple and Compound Microscope (Introduction and Uses)

Simple Microscope:

• A simple microscope is just a magnifying lens (like a magnifying glass).
• It has a single lens and produces a magnified image by bending the light rays.
• Uses: Used for viewing small objects such as stamps, insects, or small print.

Compound Microscope:

• A compound microscope uses two lenses: the objective lens (which is close to the object) and the eyepiece (which you look through).
• Magnification is produced by the combination of both lenses.
• Formula for magnification (M): $$M = M_o \times M_e$$ Where:
  • $M_o$ = Magnification due to the objective lens
  • $M_e$ = Magnification due to the eyepiece

Uses:

• Biology: For studying cells, microorganisms, and tissue samples.
• Medical: Used by pathologists and doctors to examine blood samples and other biological tissues.

---

Summary of Key Concepts:

• Reflection: Light bounces off surfaces (angle of incidence = angle of reflection).
• Refraction: Light bends when passing from one medium to another (Snell’s Law).
• Lens Formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$.
• Power of Lens: $P = \frac{1}{f}$ (measured in diopters).
• Total Internal Reflection: Occurs when light is trapped inside a medium (angle of incidence > critical angle).
• Applications of TIR: Optical fibers, endoscopes, and light guides.
• Optical Instruments: Simple microscopes (magnifying glass) and compound microscopes (used in biological studies).

---

Numerical Example on Reflection and Refraction:

Problem: A light ray strikes a glass surface (refractive index = 1.5) at an angle of 30°. Calculate the angle of refraction if the ray is moving from air (refractive index = 1) into the glass.

Solution: Using Snell’s Law:

$$\frac{\sin i}{\sin r} = \frac{n_2}{n_1}$$

Substitute values:

$$\frac{\sin 30^\circ}{\sin r} = \frac{1.5}{1}$$ $$\frac{0.5}{\sin r} = 1.5 \quad \Rightarrow \quad \sin r = \frac{0.5}{1.5} = 0.333$$
$$r = \sin^{-1}(0.333) \approx 19.47^\circ$$

Answer: The angle of refraction is approximately 19.47°.

Stay Connected & Get More Notes!

I hope these notes help you prepare and perform well in your exams. If you have any questions, feel free to reach out!

Join Our Group for More Updates and Notes:
Telegram: Join Now
WhatsApp: Join Now

Good luck with your studies! 📚