Heat and Light

Overview

Heat and Light forms a critical portion of the Physics section in GTET Paper-2 (Mathematics and Science). This topic tests your understanding of fundamental thermal concepts and optical phenomena that students encounter in classes 6-8. Questions typically assess conceptual clarity rather than complex calculations.

For the exam, you must understand how heat transfers between objects, the relationship between temperature and heat, and how light behaves when it encounters different surfaces and media. Optical concepts like reflection, refraction, and lens properties are frequently tested through diagram-based and application questions. Mastering this topic also strengthens your ability to teach these concepts through everyday examples—a key pedagogical skill tested indirectly.

Expect 3-5 questions from this combined topic. Focus on definitions, laws, ray diagrams, and real-life applications rather than numerical derivations.

Key Concepts

• **Heat vs Temperature**: Heat is the total kinetic energy of molecules (measured in Joules or calories), while temperature measures the average kinetic energy (measured in °C, °F, or K). Heat flows from higher to lower temperature, not from "more heat" to "less heat."

• **Three modes of heat transfer**: Conduction (through direct contact in solids), convection (through fluid movement in liquids/gases), and radiation (through electromagnetic waves, no medium needed).

• **Thermal expansion**: Most substances expand when heated. Solids expand least, liquids more, gases most. This principle explains gaps in railway tracks and the working of thermometers.

• **Laws of reflection**: (1) Incident ray, reflected ray, and normal lie in the same plane. (2) Angle of incidence equals angle of reflection (∠i = ∠r).

• **Refraction**: Bending of light when it passes from one medium to another due to change in speed. Light bends toward the normal when entering a denser medium, away when entering a rarer medium.

• **Refractive index**: n = speed of light in vacuum / speed of light in medium. Higher refractive index means denser optical medium.

• **Lenses**: Convex (converging) lenses are thicker in the middle; concave (diverging) lenses are thinner in the middle. Each forms different types of images depending on object position.

• **Total internal reflection**: Occurs when light travels from denser to rarer medium at an angle greater than the critical angle. Basis of optical fibers and diamond sparkle.

Formulas / Key Facts

| Concept | Formula/Fact | |---------|--------------| | Heat absorbed/released | Q = m × c × ΔT (mass × specific heat × temperature change) | | Specific heat of water | 4.18 J/g°C or 1 cal/g°C (highest among common substances) | | Celsius to Kelvin | K = °C + 273 | | Celsius to Fahrenheit | °F = (9/5)°C + 32 | | Law of reflection | ∠i = ∠r | | Snell's Law (refraction) | n₁ sin θ₁ = n₂ sin θ₂ | | Refractive index | n = c/v = real depth / apparent depth | | Lens formula | 1/f = 1/v - 1/u | | Magnification | m = v/u = height of image / height of object | | Power of lens | P = 1/f (in dioptres when f is in metres) | | Sign convention | Distances measured from optical centre; same direction as incident light is positive |

Worked Examples

**Example 1: Heat Calculation**

*Question*: How much heat is required to raise the temperature of 500 g of water from 20°C to 80°C? (Specific heat of water = 4.2 J/g°C)

*Solution*:

• Given: m = 500 g, c = 4.2 J/g°C, ΔT = 80 - 20 = 60°C
• Using Q = m × c × ΔT
• Q = 500 × 4.2 × 60
• Q = 126,000 J = 126 kJ

**Example 2: Refraction**

*Question*: A ray of light passes from air into glass (n = 1.5) at an angle of incidence of 30°. Find the angle of refraction.

*Solution*:

• Using Snell's Law: n₁ sin θ₁ = n₂ sin θ₂
• 1 × sin 30° = 1.5 × sin θ₂
• 0.5 = 1.5 × sin θ₂
• sin θ₂ = 0.5/1.5 = 0.333
• θ₂ = 19.5° (approximately)
• The ray bends toward the normal as it enters the denser medium.

**Example 3: Lens Power**

*Question*: A convex lens has a focal length of 25 cm. What is its power?

*Solution*:

• Convert focal length to metres: f = 25 cm = 0.25 m
• Power P = 1/f = 1/0.25 = +4 D
• Positive sign indicates converging lens.

Common Mistakes

• **Confusing heat and temperature** → Remember: a bucket of warm water has more heat than a cup of boiling water, but lower temperature. Heat depends on mass; temperature does not.

• **Mixing up convex and concave lenses** → Convex = converging = thicker middle = used in magnifying glass and hypermetropia correction. Concave = diverging = thinner middle = used in myopia correction. Draw the shape to remember.

• **Forgetting sign conventions in lens problems** → Always use the New Cartesian Convention: object distance (u) is negative when object is on left; focal length is positive for convex, negative for concave.

• **Assuming light always bends toward normal** → Light bends toward normal only when entering a denser medium. When going from glass to air (denser to rarer), it bends away from normal.

• **Ignoring units in power calculation** → Power in dioptres requires focal length in metres. If f = 20 cm, convert to 0.2 m before calculating P = 1/f.

• **Confusing real and virtual images** → Real images are formed by actual convergence of rays (can be caught on screen), virtual images are formed by apparent divergence (cannot be caught on screen). Plane mirrors always form virtual images.

Quick Reference

• Heat transfers: Conduction (solids) → Convection (fluids) → Radiation (no medium)

• ∠i = ∠r for reflection; image in plane mirror is virtual, erect, same size, laterally inverted

• Light bends toward normal when slowing down (entering denser medium)

• Convex lens: real inverted image (except when object within F); Concave lens: always virtual, erect, diminished

• Power = 1/focal length (metres); +ve for convex, -ve for concave

• Critical angle exists only for denser-to-rarer transition; beyond it, total internal reflection occurs