Laws of Reflection & Refraction

Laws of Reflection & Refraction

Laws of Reflection

1. The Incident Ray, Reflected Ray, and Normal: The incident ray, reflected ray, and normal to the reflecting surface at the incident point all lie in the same plane.

2. Angle of Reflection: The angle of reflection is equal to the angle of incidence.

Reflection from a Plane Mirror

1. Image Characteristics: The image is virtual and laterally inverted.

2. Size of the Image: The size of the image is equal to that of the object.

3. Distance of Image: The distance of the image from the mirror is equal to the distance of the object from the mirror.

4. Image Movement: If an object moves towards (or away from) a plane mirror with speed v, the image moves towards (or away from) it with a speed of 2v relative to the object.

5. Mirror Rotation: If a plane mirror is rotated by an angle θ, keeping the incident ray fixed, the reflected ray is rotated by an angle 2θ.

6. Full Image Requirement: To see his full image in a plane mirror, a person requires a mirror of at least half of his height.

7. Images Formed by Two Mirrors: If two plane mirrors are inclined to each other at an angle θ, the number of images (n) of a point object formed is determined as follows:

   • (a) If θ is an even integer, then n = 360°/θ - 1

   • (b) If θ is an odd integer, then n = 360°/θ if the object is symmetrically placed, and n = 360°/θ - 1 if the object is not symmetrically placed.

   • (c) If θ is a fraction, then n is equal to the integral part.

8. Focal Length: The focal length of a plane mirror is infinite.

Reflection from a Spherical Mirror

Types of Spherical Mirrors:

1. Concave Mirror

2. Convex Mirror

Position & Nature of Image Formed by a Spherical Mirror

Note: An image formed by a convex mirror is always virtual, erect, and diminished.

Uses of Concave Mirrors:

1. Shaving Glass: Used as a shaving mirror.

2. Vehicle Headlights: Reflector for vehicle headlights and searchlights.

3. Ophthalmoscope: Used in the medical field to examine the eye, ear, and nose.

4. Solar Cookers: Used in solar cookers for concentrating sunlight.

5. Focusing Light: Concentrating light at a specific spot.

Uses of Convex Mirrors:

1. Rear View Mirrors: Used as rear-view mirrors in vehicles because they provide the maximum rear field of view, and the image formed is always erect.

2. Sodium Reflector Lamp: Used in sodium reflector lamps.

Refraction of Light

Refraction is the phenomenon where a ray of light propagating in one medium enters another medium, causing a deviation from its path. This change occurs at the boundary between two media when light passes from one medium to another.

• From Rarer to Denser Medium: When light enters a denser medium (e.g., from water to glass), it deviates towards the normal at the boundary.

• From Denser to Rarer Medium: Similarly, when light passes from a denser medium to a rarer medium (e.g., from glass to air), it deviates away from the normal.

• Normal Incident Light: If light strikes the boundary normal to the surface, it enters the second medium undeviated.

Laws of Refraction

1. Plane of Refraction: The incident ray, refracted ray, and normal drawn at the incident point always lie in the same plane.

2. Snell’s Law: For a given color of light, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This constant is called the refractive index of the second medium with respect to the first medium.

   sin⁡isin⁡r=constant\frac{\sin i}{\sin r} = \text{constant} sinrsini​=constant

• Absolute Refractive Index: Defined as the ratio of the speed of light in a vacuum to the speed of light in the given medium.

  n=cvn = \frac{c}{v} n=vc​

• Refractive Index for Different Colors: The refractive index of a medium varies for different colors. It is maximum for violet light and minimum for red light.

• Temperature Effect: The refractive index decreases with increasing temperature, though the variation is small.

Some Illustrations of Refraction:

1. Bending of a Linear Object in Liquid: A linear object partially dipped in a liquid, inclined to the surface of the liquid, bends.

2. Twinkling of Stars: Stars appear to twinkle due to atmospheric refraction.

3. Oval Shape of the Sun: The sun appears oval in the morning and evening.

4. Apparent Depth of Objects: An object in a denser medium appears to be at a smaller depth when viewed from a rarer medium.

   • A fish in a pond appears at a smaller depth when viewed from the air.

   • A coin at the base of a water-filled vessel appears raised.

   • A water tank appears shallower when viewed from above.

Critical Angle and Total Internal Reflection

1. Critical Angle: The angle of incidence for which the angle of refraction is 90° is called the critical angle when light propagates from a denser to a rarer medium.

2. Total Internal Reflection: When light propagates from a denser medium towards a rarer medium, and the angle of incidence exceeds the critical angle, all the light is reflected in the denser medium.

Conditions for Total Internal Reflection:

• Light must be propagating from a denser to a rarer medium.

• The angle of incidence must exceed the critical angle.

Applications of Total Internal Reflection:

1. Sparkling of a Diamond: The brilliance of a diamond is due to total internal reflection.

2. Mirage and Looming: These phenomena occur due to total internal reflection.

3. Shining of Air Bubbles: Air bubbles in water shine due to total internal reflection.

4. Increase in Duration of Sun’s Visibility: The sun is visible before sunrise and after sunset due to total internal reflection.

5. Shining of a Smoked Ball or a Metal Ball: When dipped in water, it shines due to total internal reflection.

6. Optical Fibers: Optical fibers use multiple total internal reflections to transmit light without loss of energy.

Refraction of Light Through Lenses

A lens is a section of transparent refractive material with two surfaces of definite geometrical shape, where one surface is spherical.

Types of Lenses:

1. Convex Lens (Converging Lens): Thicker in the middle than at the edges.

2. Concave Lens (Diverging Lens): Thicker at the edges than in the middle.

Key Terms Related to Lenses:

• Optical Centre

• First Focus

• Principal Axis

• Second Focus

Final Thoughts

From plane mirrors that help us see our reflections to concave and convex mirrors used in everyday objects like vehicle mirrors and shaving mirrors, these principles are deeply embedded in our daily lives.

Additionally, the concept of refraction helps us understand how light behaves when it enters different media, impacting everything from the way we see objects underwater to the technology behind optical fibers used in communication.

By mastering these foundational principles of light, we not only prepare for exams but also gain a deeper appreciation for the science that powers everything from medical devices to modern telecommunications. At our institute, we aim to make these complex ideas relatable and easy to understand, ensuring that you can connect the dots between theory and real-world applications.