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Light - Reflection and Refraction — Question 12

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Question 12

An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

Answer

Given,

f = +15 cm

u = -10 cm

v = ?

According to the mirror formula,

1v\dfrac{1}{v} + 1u\dfrac{1}{u} = 1f\dfrac{1}{f}

Substituting the values we get,

1v+1−10=115⇒1v=110+115⇒1v=3+230⇒1v=530⇒1v=16⇒v=6 cm\dfrac{1}{v} + \dfrac{1}{-10} = \dfrac{1}{15} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{1}{ 10} + \dfrac{1}{15} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{3+2}{30} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{5}{30} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{1}{6} \\[1em] \Rightarrow v = 6\text{ cm}

Therefore, image is formed 6 cm behind the mirror. Image is virtual and erect.

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Science | Chapter 9: Light: Reflection and RefractionWeb Content

Chapter 9: Light: Reflection and Refraction — Quick Revision Guide

Introduction

Light behaves predictably when it reflects off mirrors and refracts through lenses. This chapter covers the laws of reflection and refraction, image formation by spherical mirrors and lenses, and numerical problem-solving using mirror and lens formulae.

Key Points at a Glance

  1. Laws of reflection: angle of incidence = angle of reflection; incident ray, reflected ray, normal in same plane
  2. Concave mirror: converging; image depends on object position (6 cases from ∞ to between P and F)
  3. Convex mirror: always virtual, erect, diminished image; used as rear-view mirror (wider field of view)
  4. Mirror formula: 1/v + 1/u = 1/f; magnification m = −v/u = h'/h
  5. Sign convention: object on left → u negative; concave f negative; convex f positive
  6. Refraction: bending of light at interface; Snell's law: sin i / sin r = n21; denser medium bends towards normal
  7. Convex lens: converging; 6 image positions; concave lens: always virtual, erect, diminished
  8. Lens formula: 1/v − 1/u = 1/f; m = v/u; Power P = 1/f(m); unit: dioptre (D)
  9. Convex lens: +f, +P; Concave lens: −f, −P; combination: P = P1 + P2

Real-World Connections

Concave mirrors in solar cookers and headlights; convex mirrors for vehicle rear-view; magnifying glass is a convex lens; spectacles correct vision defects; cameras and projectors use lenses.

Quick Self-Test (5 Questions)

  1. What is the most important concept you learned from this chapter?
  2. Can you write three key equations/formulae from this chapter from memory?
  3. Draw a labelled diagram relevant to this chapter without looking at your notes.
  4. Explain one real-world application of a concept from this chapter.
  5. What is one common mistake students make in this chapter, and how can you avoid it?

Further Study

  • NCERT Textbook Chapter 9
  • NCERT Exemplar Problems
  • Bright Tutorials Detailed Notes: ch09-light-reflection-refraction.html
  • Bright Tutorials Practice Questions: ch09-light-reflection-refraction.html
  • Previous Year CBSE Board Papers

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