Reflection and Refraction of Light (Class 10): Mirrors, Lenses, Laws & Numericals

Reflection and Refraction of Light: Concepts, Laws and Solved Examples

Why does a spoon look bent when dipped in a glass of water? Why does a car's side mirror say "objects are closer than they appear"? The answers lie in two fundamental properties of light: reflection and refraction. These topics carry significant weight in Class 10 board exams and are also part of the foundation for optics studied later in Class 12.

---

What Is Light?

Light is a form of electromagnetic energy that enables us to see objects. It travels in straight lines, has a speed of approximately 3 × 10⁸ m/s in vacuum, and exhibits both wave and particle properties.

---

Reflection of Light

Reflection is the phenomenon in which light bounces back into the same medium after striking a smooth surface like a mirror.

Laws of Reflection

• The angle of incidence equals the angle of reflection (∠i = ∠r).
• The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.

---

Spherical Mirrors

A spherical mirror is a part of a hollow sphere whose inner or outer surface is polished.

• Concave mirror: Reflecting surface curves inward. Used in shaving mirrors, headlights, and telescopes.
• Convex mirror: Reflecting surface curves outward. Used as rear-view mirrors in vehicles.

Key Terms

• Centre of curvature (C): Centre of the sphere of which the mirror is a part.
• Focus (F): Point where parallel rays converge (or appear to diverge from).
• Focal length (f): Distance between pole and focus. f = R/2.

Mirror Formula

1/v + 1/u = 1/f

where v = image distance, u = object distance, and f = focal length.

Magnification

m = h_i / h_o = − v / u

Solved Numerical 1

Question: An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find the position of the image.

Solution:
u = −30 cm, f = −20 cm
1/v + 1/(−30) = 1/(−20)
1/v = −1/20 + 1/30 = (−3 + 2)/60 = −1/60
v = −60 cm (image is real, inverted, and on the same side).

---

Refraction of Light

Refraction is the bending of light as it passes from one transparent medium to another due to a change in speed.

Laws of Refraction

• The incident ray, the refracted ray, and the normal lie in the same plane.
• The ratio of sine of the angle of incidence to sine of angle of refraction is constant. This is Snell's Law:

sin i / sin r = n

where n is the refractive index of the second medium with respect to the first.

Refractive Index

n = c / v

where c is the speed of light in vacuum, and v is the speed in the given medium. The higher the refractive index, the slower the light moves in that medium.

Solved Numerical 2

Question: The speed of light in glass is 2 × 10⁸ m/s. Find its refractive index.

Solution:
n = c / v = (3 × 10⁸) / (2 × 10⁸) = 1.5

---

Lenses

A lens is a transparent medium bounded by two surfaces, at least one of which is curved.

• Convex (converging) lens: Thicker in the middle. Converges parallel rays to a focus.
• Concave (diverging) lens: Thinner in the middle. Diverges parallel rays.

Lens Formula

1/v − 1/u = 1/f

Power of a Lens

P = 1 / f (in metres), measured in dioptres (D).

Solved Numerical 3

Question: Find the power of a convex lens of focal length 25 cm.

Solution:
f = 25 cm = 0.25 m
P = 1 / 0.25 = +4 D

---

Real-Life Applications

• Spectacles correct vision defects using convex or concave lenses.
• Cameras use lenses to focus light on film or sensors.
• Periscopes use plane mirrors to see over obstacles.
• Optical fibres in telecommunications work on total internal reflection.

---

Sign Conventions (Cartesian System)

• All distances are measured from the pole/optical centre.
• Distances measured in the direction of incident light are positive.
• Heights above the principal axis are positive; below are negative.

---

Common Mistakes Students Make

• Forgetting to apply sign conventions in mirror and lens problems.
• Confusing concave mirrors with concave lenses.
• Forgetting that refractive index has no unit.

---

Frequently Asked Questions

Q1. Why does a swimming pool look shallower than it actually is?
Because of refraction. Light from the bottom bends away from the normal as it leaves water, making the pool appear less deep.

Q2. Can a virtual image be photographed?
Yes. Although virtual images cannot be projected on a screen, a camera (which itself uses a converging lens) can capture them.

Q3. What is the difference between reflection and refraction?
Reflection bounces light back into the same medium, while refraction transmits light into a new medium with a change in direction.

Q4. Why are convex mirrors used as rear-view mirrors?
They produce small, upright, virtual images and provide a wider field of view than plane mirrors.

Q5. What does a power of −2 D mean?
The lens is concave with a focal length of −50 cm.

---

Key Takeaways

Reflection and refraction explain how mirrors, lenses, cameras, and even our eyes work. Mastering ray diagrams, sign conventions, and the mirror and lens formulas will help you solve almost every numerical in Class 10 board exams and lay a strong base for advanced optics in Class 11 and 12.