MP Board Class 10 Science Chapter 9: Light – Reflection a…

Chapter 9: Light — Reflection and Refraction is a high-weightage chapter in MP Board Class 10 Science, contributing 10–12 marks in the annual board exam. This chapter covers the nature of light, reflection by spherical mirrors, image formation using ray diagrams, mirror formula, refraction through glass slabs and lenses, lens formula, and the concept of power of lenses. Questions range from 1-mark MCQs to 5-mark numerical and ray diagram problems. Mastering mirror and lens formulae is essential for board success.

🪞 Reflection of Light

Light is a form of energy that travels in straight lines. When light falls on a surface and bounces back into the same medium, it is called reflection. The laws of reflection govern this phenomenon and apply to all reflecting surfaces — plane mirrors as well as spherical mirrors.

📜 Laws of Reflection

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

📊 Properties of Images Formed by a Plane Mirror

Property	Characteristic
Nature	Virtual and erect
Size	Same size as object
Distance	Same distance behind the mirror as object is in front
Lateral Inversion	Left appears right and vice versa

🔮 Spherical Mirrors — Concave & Convex

Spherical mirrors are mirrors with curved reflecting surfaces. If the reflecting surface is curved inward, it is a concave mirror (converging). If the reflecting surface bulges outward, it is a convex mirror (diverging). Key terms: centre of curvature (C), pole (P), principal axis, focus (F), and focal length (f = R/2).

📊 Comparison: Concave vs Convex Mirror

Feature	Concave Mirror	Convex Mirror
Shape	Curved inward (like a cave)	Curved outward (bulging)
Focus	Real focus (in front of mirror)	Virtual focus (behind mirror)
Nature of image	Real/virtual depending on object position	Always virtual, diminished, erect
Uses	Torches, shaving mirrors, headlights, solar furnaces	Rear-view mirrors in vehicles, CCTV

📌 Image Formation by Concave Mirror — Summary Table

Position of Object	Position of Image	Nature	Size
At infinity	At focus (F)	Real, inverted	Highly diminished
Beyond C	Between F and C	Real, inverted	Diminished
At C	At C	Real, inverted	Same size
Between F and C	Beyond C	Real, inverted	Enlarged
At F	At infinity	Real, inverted	Highly enlarged
Between P and F	Behind the mirror	Virtual, erect	Enlarged

📐 Mirror Formula & Magnification

The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror. It is a critical tool for solving numerical problems in MP Board exams.

Mirror Formula

1/f = 1/v + 1/u

Where: f = focal length, v = image distance, u = object distance

Magnification (m)

m = h_i / h_o = -v / u

Where: h_i = image height, h_o = object height

Sign Convention (Cartesian)

All distances are measured from the pole of the mirror.
Distances measured in the direction of incident light (towards mirror) are negative.
Distances measured opposite to incident light (behind mirror) are positive.
Heights above the principal axis are positive; below are negative.
For concave mirrors: f = −ve (negative)
For convex mirrors: f = +ve (positive)

🔢 Solved Example

Example: An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the position and nature of the image.

Solution:
u = −15 cm (object in front), f = −10 cm (concave mirror)
Using 1/f = 1/v + 1/u → 1/v = 1/f − 1/u = 1/(−10) − 1/(−15)
1/v = −1/10 + 1/15 = (−3 + 2)/30 = −1/30
v = −30 cm (negative means image is in front → real image)
Magnification m = −v/u = −(−30)/(−15) = −2 (inverted, enlarged 2×)
Answer: Image is real, inverted, magnified 2×, and located 30 cm in front of the mirror.

💧 Refraction of Light

When light travels from one transparent medium to another, it changes direction — this is called refraction. This happens because light travels at different speeds in different media. The bending depends on the refractive indices of the two media.

Laws of Refraction

The incident ray, the refracted ray, and the normal at the interface all lie in the same plane.
Snell’s Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media. sin i / sin r = n (refractive index of second medium relative to first)

📊 Refractive Index of Common Substances

Medium	Refractive Index	Optical Density
Air	1.0003 (~1)	Lowest
Water	1.33	Medium
Glass (crown)	1.52	High
Diamond	2.42	Highest

Refraction through a Glass Slab

When light passes through a rectangular glass slab, it undergoes refraction twice — once entering and once exiting. The emergent ray is parallel to the incident ray but laterally displaced. This lateral shift depends on the thickness of the slab, refractive index, and angle of incidence.

🔢 Refractive Index Formula

n = c / v

Where: n = refractive index, c = speed of light in vacuum (3 × 10⁸ m/s), v = speed of light in the medium

Absolute refractive index of a medium = speed of light in vacuum / speed of light in that medium. The refractive index of medium 2 relative to medium 1 is: n₂₁ = n₂ / n₁ = v₁ / v₂.

🔍 Lens Formula & Power of Lens

A lens is a transparent refracting medium bounded by two curved surfaces. Convex lenses (converging) are thicker in the middle, while concave lenses (diverging) are thinner in the middle. The lens formula and power calculations are frequently tested in MP Board exams.

Lens Formula

1/f = 1/v − 1/u

Where: f = focal length, v = image distance (from optical centre), u = object distance

Sign convention for lenses: u is always negative (object on left). For convex lens, f = +ve. For concave lens, f = −ve. v is positive for real images (right side) and negative for virtual images (left side).

Magnification by Lenses

m = h_i / h_o = v / u

Power of a Lens

The power of a lens is the measure of its ability to converge or diverge light rays. It is defined as the reciprocal of the focal length (in metres).

P = 1 / f (in metres)

SI unit of power is dioptre (D). 1 D = 1 m⁻¹. Convex lens: P = +ve. Concave lens: P = −ve.

📊 Image Formation by Convex Lens

Object Position	Image Position	Nature
At infinity	At focus (F)	Real, inverted, diminished
Beyond 2F	Between F and 2F	Real, inverted, diminished
At 2F	At 2F	Real, inverted, same size
Between F and 2F	Beyond 2F	Real, inverted, enlarged
At focus (F)	At infinity	Real, inverted, highly enlarged
Between F and O	On same side as object	Virtual, erect, enlarged

📝 Practice Questions with Answers

Q1. Numerical Based

An object is placed at a distance of 20 cm from a concave mirror of focal length 12 cm. Find the image distance, magnification, and nature of the image.

Answer: u = −20 cm, f = −12 cm. Using 1/f = 1/v + 1/u: 1/v = 1/(−12) − 1/(−20) = −1/12 + 1/20 = (−5+3)/60 = −2/60 = −1/30. So v = −30 cm. Image is 30 cm in front of mirror (real). m = −v/u = −(−30)/(−20) = −1.5. Image is real, inverted, and 1.5× magnified.

Q2. Refractive Index

The speed of light in water is 2.25 × 10⁸ m/s and in glass is 2.0 × 10⁸ m/s. Calculate the refractive index of glass with respect to water. In which medium does light bend towards the normal?

Answer: n_gw = v_water / v_glass = 2.25 × 10⁸ / 2.0 × 10⁸ = 1.125. Since n_gw > 1, glass is optically denser than water. Light bends towards the normal when going from water to glass.

Q3. Power of Lens

A convex lens has a focal length of 25 cm. Calculate its power. What is the nature and power of a lens whose focal length is −50 cm?

Answer: For convex lens, f = 25 cm = 0.25 m. P = 1/f = 1/0.25 = +4 D. For f = −50 cm = −0.5 m, P = 1/(−0.5) = −2 D. This is a concave lens (negative power).

Q4. Mirror Application

A convex mirror has a focal length of 20 cm. An object is placed 30 cm from the mirror. Find the image distance and magnification. Why are convex mirrors preferred as rear-view mirrors?

Answer: For convex mirror, f = +20 cm (sign convention), u = −30 cm. Using 1/f = 1/v + 1/u: 1/v = 1/20 − 1/(−30) = 1/20 + 1/30 = 5/60 = 1/12. So v = +12 cm (behind mirror, virtual). m = −v/u = −12/(−30) = +0.4. Image is virtual, erect, and diminished (0.4×). Convex mirrors are preferred because they give a wider field of view and always form erect, diminished images, helping drivers see more traffic behind them.

Q5. Lens Application

An object is placed 15 cm from a convex lens of focal length 10 cm. Find the image position, magnification, and nature. Draw the ray diagram.

Answer: u = −15 cm, f = +10 cm (convex). Using 1/f = 1/v − 1/u: 1/v = 1/f + 1/u = 1/10 + 1/(−15) = 1/10 − 1/15 = (3−2)/30 = 1/30. So v = +30 cm (real image, right side). m = v/u = 30/(−15) = −2. Image is real, inverted, and magnified 2×. Ray diagram: (1) ray parallel to axis refracts through F, (2) ray through optical centre goes straight. Both meet 30 cm on the other side.

📋 Previous Year Questions (2017–2026)

Year	Question	Marks
2026	Define power of a lens. A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 30 cm. Find the power of the combination. Is the combination converging or diverging?	3
2025	An object is placed at a distance of 30 cm from a concave mirror. The image formed is three times the size of the object. Calculate the focal length of the mirror in both cases — when the image is real and when it is virtual.	5
2024	State Snell’s law of refraction. Light enters from air to glass having refractive index 1.52. What is the speed of light in glass? (Speed of light in air = 3 × 10⁸ m/s)	3

📌 PYQ Solutions

2026 Solution: P_convex = 1/0.20 = +5 D. P_concave = 1/(−0.30) = −3.33 D. P_total = 5 − 3.33 = +1.67 D. Since total power is positive, the combination behaves as a converging lens.

2025 Solution: u = −30 cm. For real image (m = −3): m = −v/u → −3 = −v/(−30) → v = −90 cm. Using 1/f = 1/v + 1/u: 1/f = 1/(−90) + 1/(−30) = −1/90 − 3/90 = −4/90 → f = −22.5 cm. For virtual image (m = +3): m = −v/u → 3 = −v/(−30) → v = +90 cm. 1/f = 1/90 + 1/(−30) = 1/90 − 3/90 = −2/90 → f = −45 cm.

2024 Solution: Snell’s law: sin i / sin r = n. Given n = 1.52, c = 3 × 10⁸ m/s. Using n = c/v → v = c/n = 3×10⁸/1.52 = 1.97 × 10⁸ m/s. Speed of light in glass = 1.97 × 10⁸ m/s.

🎯 Exam Tips for 2027

🔢 Master sign conventions: Use the Cartesian sign convention consistently for all numerical problems. Mixing signs is the #1 reason for wrong answers.
📐 Practice ray diagrams: Draw at least 2 rays for every case — the parallel ray and the focal ray. MP Board often awards 1–2 marks for correct ray diagrams in 5-mark questions.
📝 Memorize key values: Refractive indices (air=1, water=1.33, glass=1.5, diamond=2.42) and speed of light (3×10⁸ m/s in vacuum) are frequently asked.
🧮 Formula revision: Write mirror formula, lens formula, magnification formula, and power formula on a single page and revise daily before the exam.
⏳ Time management: Allocate maximum 15 minutes for numerical problems. For 5-mark questions, spend 2 min reading, 8 min solving, 5 min reviewing.
📊 Common mistakes to avoid: Forgetting to convert cm to m for power calculation, using the wrong sign for concave vs convex mirrors, confusing mirror and lens formulae.