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Physics · Class 12 Science

Ch 2Ray Optics and Optical Instruments — Class 12 Physics, concept-first.

Light is the part of the electromagnetic spectrum that our eyes can detect. It lies in a narrow wavelength range: from about to . This is what allows us to see and understand the world.

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Key concepts

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Partial Mirror Obstruction

Imagine you are standing in front of a full-length mirror. You see your entire body. Now imagine someone places a large cardboard sheet in front of the mirror, covering the bottom half.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

9.1

Introduction

Light is the part of the electromagnetic spectrum that our eyes can detect. It lies in a narrow wavelength range: from about to . This is what allows us to see and understand the world.

9.2

Reflection of Light by Spherical Mirrors

The laws of reflection hold for every point on a spherical mirror, just as they do for a plane mirror.

9.2.1

Sign Convention

To derive a single formula that works for all cases of reflection by spherical mirrors and refraction by spherical lenses, we must first agree on how to measure distances and heights.

9.2.2

Focal Length of Spherical Mirrors

When a parallel beam of light (rays coming from a very distant object) falls on a spherical mirror, the behaviour depends on the mirror type:

9.2.3

The Mirror Equation

The mirror equation is the fundamental relationship that links three key distances for any spherical mirror (concave or convex):

+Worked Examplesi4 questions
  1. Example 9.1Suppose that the lower half of the concave mirror's reflecting surface in Fig. 9.6 is covered with an opaque (non-reflective) material. ![Fi…Free
  2. Example 9.2A mobile phone lies along the principal axis of a concave mirror, as shown in Fig. 9.7. Show by suitable diagram, the formation of its image…Free
  3. Example 9.3An object is placed at (i) $10\ \text{cm}$, (ii) $5\ \text{cm}$ in front of a concave mirror of radius of curvature $15\ \text{cm}$. Find th…Preview
  4. Example 9.4Suppose while sitting in a parked car, you notice a jogger approaching towards you in the side view mirror of $R = 2\ \text{m}$. If the jogg…Preview
9.3

Refraction

When light travelling in one transparent medium meets another transparent medium, part of it enters the second medium.

9.4

Total Internal Reflection

When light travels from an optically denser medium (like water or glass) into a rarer medium (like air), it bends away from the normal. This bending is called refraction.

9.4.1

Total Internal Reflection in Nature and its Technological Applications

Total internal reflection (TIR) is not just a textbook phenomenon — it is the working principle behind several everyday devices and natural effects.

9.5

Refraction at Spherical Surfaces and by Lenses

When light passes from one transparent medium to another through a spherical interface, the surface is curved.

9.5.1

Refraction at a Spherical Surface

When light travels from one transparent medium to another across a curved spherical surface, the path of the rays bends.

+Worked Examplesi1 question
  1. Example 9.5Light from a point source in air falls on a spherical glass surface ($n = 1.5$ and radius of curvature $= 20\ \text{cm}$). The distance of t…Preview
9.5.2

Refraction by a Lens

A lens forms an image by refracting light at two spherical surfaces. The process is broken into two steps:

+Worked Examplesi1 question
  1. Example 9.6A magician during a show makes a glass lens with $n = 1.47$ disappear in a trough of liquid. What is the refractive index of the liquid? Cou…Preview
9.5.3

Power of a Lens

The power of a lens tells us how strongly it bends light. - A lens with short focal length bends light a lot — it converges (convex) or diverges (concave) the rays sharply.

+Worked Examplesi1 question
  1. Example 9.7(i) If $f = 0.5\ \text{m}$ for a glass lens, what is the power of the lens? (ii) The radii of curvature of the faces of a double convex lens…Preview
9.5.4

Combination of Thin Lenses in Contact

A single lens has limitations: its focal length is fixed, and it may produce images with aberrations (blurring).

+Worked Examplesi1 question
  1. Example 9.8Find the position of the image formed by the lens combination given in the Fig. 9.20. ![Figure 9.20](/figures/ray-optics-and-optical-instrum…Preview
9.6

Refraction through a Prism

When light passes through a triangular prism, it bends twice — once entering and once leaving. The net effect is a deviation of the ray from its original path.

9.7

Optical Instruments

The human eye is a natural optical instrument. It uses a lens to form a real, inverted image on the retina.

9.7.1

The Microscope

A simple microscope is just a converging lens of small focal length. It is held close to the object (at a distance less than or equal to the focal length) to produce an erect, virtual, and magnified i…

9.7.2

Telescope

A telescope is an optical instrument designed to make distant objects appear closer and larger. Unlike a microscope, which magnifies small nearby objects, a telescope increases the angular size of a d…

Summary

- Reflection of Light: Laws: incident, reflected, and normal lie in same plane; . For a plane mirror, image is virtual, erect, same size, and laterally inverted.

Points to Ponder

1. Reflection and refraction laws are universal. The laws of reflection and refraction apply at the point of incidence for any surface shape and any pair of media — they are not limited to flat surfac…

Exercises

+Show 31 questions31 questions
  1. 9.1A small candle, $2.5\ \text{cm}$ in size is placed at $27\ \text{cm}$ in front of a concave mirror of radius of curvature $36\ \text{cm}$. A…Free
  2. 9.2A $4.5\ \text{cm}$ needle is placed $12\ \text{cm}$ away from a convex mirror of focal length $15\ \text{cm}$. Give the location of the imag…Free
  3. 9.3A tank is filled with water to a height of $12.5\ \text{cm}$. The apparent depth of a needle lying at the bottom of the tank is measured by…Free
  4. 9.4Figures 9.27(a) and (b) show refraction of a ray in air incident at $60^\circ$ with the normal to a glass-air and water-air interface, respe…Preview
  5. 9.5A small bulb is placed at the bottom of a tank containing water to a depth of $80\ \text{cm}$. What is the area of the surface of water thro…Preview
  6. 9.6A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum devi…Preview
  7. 9.7Double-convex lenses are to be manufactured from a glass of refractive index $1.55$, with both faces of the same radius of curvature. What i…Preview
  8. 9.8A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam $12\ \text{cm}$ from P. At what point does t…Preview
  9. 9.9An object of size $3.0\ \text{cm}$ is placed $14\ \text{cm}$ in front of a concave lens of focal length $21\ \text{cm}$. Describe the image…Preview
  10. 9.10What is the focal length of a convex lens of focal length $30\ \text{cm}$ in contact with a concave lens of focal length $20\ \text{cm}$? Is…Preview
  11. 9.11A compound microscope consists of an objective lens of focal length $2.0\ \text{cm}$ and an eyepiece of focal length $6.25\ \text{cm}$ separ…Preview
  12. 9.12A person with a normal near point ($25\ \text{cm}$) using a compound microscope with objective of focal length $8.0\ \text{mm}$ and an eyepi…Preview
  13. 9.13A small telescope has an objective lens of focal length $144\ \text{cm}$ and an eyepiece of focal length $6.0\ \text{cm}$. What is the magni…Preview
  14. 9.14(a) A giant refracting telescope at an observatory has an objective lens of focal length $15\ \text{m}$. If an eyepiece of focal length $1.0…Preview
  15. 9.15Use the mirror equation to deduce that: (a) an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$. (b)…Preview
  16. 9.16A small pin fixed on a table top is viewed from above from a distance of $50\ \text{cm}$. By what distance would the pin appear to be raised…Preview
  17. 9.17(a) Figure 9.28 shows a cross-section of a 'light pipe' made of a glass fibre of refractive index $1.68$. The outer covering of the pipe is…Preview
  18. 9.18The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall $3\ \text{m}$ away by means of a large…Preview
  19. 9.19A screen is placed $90\ \text{cm}$ from an object. The image of the object on the screen is formed by a convex lens at two different locatio…Preview
  20. 9.20(a) Determine the 'effective focal length' of the combination of the two lenses in Exercise 9.10, if they are placed $8.0\ \text{cm}$ apart…Preview
  21. 9.21At what angle should a ray of light be incident on the face of a prism of refracting angle $60^\circ$ so that it just suffers total internal…Preview
  22. 9.22A card sheet divided into squares each of size $1\ \text{mm}^2$ is being viewed at a distance of $9\ \text{cm}$ through a magnifying glass (…Preview
  23. 9.23(a) At what distance should the lens be held from the card sheet in Exercise 9.22 in order to view the squares distinctly with the maximum p…Preview
  24. 9.24What should be the distance between the object in Exercise 9.23 and the magnifying glass if the virtual image of each square in the figure i…Preview
  25. 9.25Answer the following questions: (a) The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual im…Preview
  26. 9.26An angular magnification (magnifying power) of $30\text{X}$ is desired using an objective of focal length $1.25\ \text{cm}$ and an eyepiece…Preview
  27. 9.27A small telescope has an objective lens of focal length $140\ \text{cm}$ and an eyepiece of focal length $5.0\ \text{cm}$. What is the magni…Preview
  28. 9.28(a) For the telescope described in Exercise 9.27 (a), what is the separation between the objective lens and the eyepiece? (b) If this telesc…Preview
  29. 9.29A Cassegrain telescope uses two mirrors as shown in Fig. 9.26. ![Figure 9.26](/figures/ray-optics-and-optical-instruments/schematic-reflecti…Preview
  30. 9.30Light incident normally on a plane mirror attached to a galvanometer coil retraces backwards as shown in Fig. 9.29. A current in the coil pr…Preview
  31. 9.31Figure 9.30 shows an equiconvex lens (of refractive index $1.50$) in contact with a liquid layer on top of a plane mirror. A small needle wi…Preview

Exemplar Problems

Higher-order thinking / exemplar-style practice problems.

+Show 32 questions32 questions
  1. Q1A ray of light incident at an angle $\theta$ on a refracting face of a prism emerges from the other face normally. If the angle of the prism…Free
  2. Q2A short pulse of white light is incident from air to a glass slab at normal incidence. After travelling through the slab, the first colour t…Free
  3. Q3An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus. The image (a) moves away…Free
  4. Q4A passenger in an aeroplane shall (a) never see a rainbow. (b) may see a primary and a secondary rainbow as concentric circles. (c) may see…Preview
  5. Q5You are given four sources of light each one providing a light of a single colour – red, blue, green and yellow. Suppose the angle of refrac…Preview
  6. Q6The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, i…Preview
  7. Q7The phenomena involved in the reflection of radiowaves by ionosphere is similar to (a) reflection of light by a plane mirror. (b) total inte…Preview
  8. Q8A ray of light PQ travels upward and to the right and strikes a concave mirror at a point Q that lies above the principal axis. The straight…Preview
  9. Q9A container holds a horizontal layer of turpentine floating on top of water, with air above the turpentine. Turpentine is optically denser t…Preview
  10. Q10A car is moving with at a constant speed of $60 \text{ km h}^{-1}$ on a straight road. Looking at the rear view mirror, the driver finds tha…Preview
  11. Q11Some materials fabricated in the laboratory (metamaterials) have a **negative** refractive index. A ray of light travels in air (medium 1) a…Preview
  12. Q12Consider an extended object immersed in water contained in a plane trough. When seen from close to the edge of the trough the object looks d…Preview
  13. Q13A square block of glass ABCD has refractive index $1.6$. The corners are arranged with A at the top-left, B at the top-right, C at the botto…Preview
  14. Q14Between the primary and secondary rainbows, there is a dark band known as Alexandar's dark band. This is because (a) light scattered into th…Preview
  15. Q15A magnifying glass is used, as the object to be viewed can be brought closer to the eye than the normal near point. This results in (a) a la…Preview
  16. Q16An astronomical refractive telescope has an objective of focal length 20m and an eyepiece of focal length 2cm. (a) The length of the telesco…Preview
  17. Q17Will the focal length of a lens for red light be more, same or less than that for blue light?Preview
  18. Q18The near vision of an average person is 25cm. To view an object with an angular magnification of 10, what should be the power of the microsc…Preview
  19. Q19An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is…Preview
  20. Q20Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of ea…Preview
  21. Q21For a glass prism ($\mu = \sqrt{3}$) the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism.Preview
  22. Q22A short object of length $L$ is placed along the principal axis of a concave mirror away from focus. The object distance is $u$. If the mirr…Preview
  23. Q23A circular disc of radius $R$ is placed horizontally and coaxially inside an opaque hemispherical bowl of radius $a$, with the disc's centre…Preview
  24. Q24A thin convex lens of focal length 25 cm is cut into two pieces 0.5 cm above the principal axis. The top part is placed at (0,0) and an obje…Preview
  25. Q25In many experimental set-ups the source and screen are fixed at a distance say $D$ and the lens is movable. Show that there are two position…Preview
  26. Q26A cylindrical jar of height $h$ is filled to the brim with a transparent liquid of refractive index $\mu$. A small dot is marked at the cent…Preview
  27. Q27A myopic adult has a far point at 0.1 m. His power of accomodation is 4 diopters. (i) What power lenses are required to see distant objects?…Preview
  28. Q28Show that for a material with refractive index $\mu \geq \sqrt{2}$, light incident at any angle shall be guided along a length perpendicular…Preview
  29. Q29The mixture a pure liquid and a solution in a long vertical column (i.e, horizontal dimensions $\ll$ vertical dimensions) produces diffusion…Preview
  30. Q30If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to…Preview
  31. Q31An infinitely long solid cylinder of radius $R$ is made of an unusual exotic material whose refractive index is exactly $-1$. The cylinder i…Preview
  32. Q32A thin lens is placed on the axis between a point source S and an observer O. The source S lies on the axis a distance $u$ to the left of th…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 2 questions2 questions
  1. Q1Define the power of a lens. Write its S.I. unit.Preview
  2. Q2(a) With the help of a ray diagram, show how a concave mirror is used to obtain an erect and magnified image of an object. (b) Using the abo…Preview