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Ray Optics and Optical Instruments

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Chapter Notes

Overview
This chapter explores the ray model of light to explain reflection, refraction, and dispersion, and applies these principles to image formation by spherical mirrors and lenses. It is a foundational chapter in physics because it bridges theoretical wave optics with practical optical instruments like microscopes and telescopes. The one big idea a student must walk away with is that using sign conventions and paraxial approximations, a single mirror equation and a single lens formula can describe all cases of image formation by spherical surfaces.
Key Concepts (22)
Ray of light
The path along which light travels in a straight line in a homogeneous medium.
e.g. A laser beam appearing as a straight line in a dusty room.
Beam of light
A bundle of rays of light.
e.g. Sunlight entering a room through a small hole forms a beam.
Pole (P)
The geometric centre of a spherical mirror.
e.g. The centre point of a concave mirror's reflecting surface.
Principal axis
The line joining the pole and the centre of curvature of a spherical mirror.
e.g. The horizontal line through the centre of a concave mirror.
Principal focus (F)
The point on the principal axis of a spherical mirror where rays parallel to the principal axis converge (concave) or appear to diverge from (convex) after reflection.
e.g. The point where sunlight focused by a concave mirror burns paper.
Focal length (f)
The distance between the pole and the principal focus of a spherical mirror.
e.g. For a concave mirror with radius 20 cm, f = 10 cm.
Focal plane
The plane through the principal focus perpendicular to the principal axis.
e.g. Rays parallel but not parallel to the principal axis converge at a point on the focal plane.
Real image
An image formed when rays actually converge at a point; can be projected on a screen.
e.g. The image formed on a screen by a concave mirror when object is beyond focus.
Virtual image
An image formed when rays appear to diverge from a point; cannot be projected on a screen.
e.g. The image of your face in a plane mirror.
Refraction
The change in direction of propagation of a ray of light when it passes obliquely from one transparent medium to another.
e.g. A pencil appearing bent in a glass of water.
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.
e.g. When light enters water from air, sin i / sin r = 1.33.
Refractive index (n)
The ratio of the speed of light in vacuum to the speed of light in a medium.
e.g. Refractive index of water is 1.33.
Total internal reflection
The complete reflection of light within a denser medium when the angle of incidence exceeds the critical angle.
e.g. Light travelling in a glass prism and reflecting internally at 45°.
Critical angle (ic)
The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.
e.g. Critical angle for water-air interface is 48.75°.
Lens maker's formula
A formula relating the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces.
e.g. Used to design a lens of desired focal length.
Power of a lens (P)
The reciprocal of the focal length in metres; measured in dioptres.
e.g. A convex lens of focal length 0.5 m has power +2 D.
Angle of deviation (δ)
The angle between the incident ray and the emergent ray when light passes through a prism.
e.g. For a thin prism, δ = (n-1)A.
Minimum deviation (Dm)
The smallest possible angle of deviation for a given prism, occurring when the ray inside the prism is parallel to its base.
e.g. Used to determine refractive index of prism material.
Optical fibre
A thin, flexible fibre with a core of higher refractive index and cladding of lower refractive index, used to transmit light via total internal reflection.
e.g. Used in endoscopy to view internal organs.
Magnification (m)
The ratio of the height of the image to the height of the object.
e.g. For a concave mirror, m = -v/u.
Lateral shift
The perpendicular distance between the incident ray and the emergent ray when light passes through a parallel-sided slab.
e.g. A ray of light passing through a glass slab emerges parallel but displaced sideways.
Apparent depth
The depth of an object in a denser medium as seen from a rarer medium, which is less than the real depth.
e.g. A coin at the bottom of a water tank appears raised.
Formulas & Equations (16)
f = R/2
Reads as: focal length equals radius of curvature divided by two
Variables: f = focal length (m), R = radius of curvature (m)
Use when: Finding focal length of a spherical mirror given its radius of curvature.
⚠ Students forget the sign; for concave mirrors both f and R are negative, for convex both are positive.
1/v + 1/u = 1/f
Reads as: one over image distance plus one over object distance equals one over focal length
Variables: v = image distance (m), u = object distance (m), f = focal length (m)
Use when: Finding image position for any spherical mirror.
⚠ Using positive values for u and v without sign convention; u is always negative for real objects.
m = h'/h = -v/u
Reads as: magnification equals height of image over height of object equals negative v over u
Variables: m = magnification, h' = image height (m), h = object height (m), v = image distance (m), u = object distance (m)
Use when: Finding size and nature (inverted/erect) of image formed by a spherical mirror.
⚠ Forgetting the negative sign; m negative means inverted image, positive means erect.
n21 = sin i / sin r
Reads as: refractive index of medium 2 with respect to medium 1 equals sine of angle of incidence over sine of angle of refraction
Variables: n21 = refractive index (no unit), i = angle of incidence (degrees), r = angle of refraction (degrees)
Use when: Calculating refractive index or finding angle of refraction.
⚠ Confusing n21 with n12; n21 = 1/n12.
sin ic = n21
Reads as: sine of critical angle equals refractive index of rarer medium with respect to denser medium
Variables: ic = critical angle (degrees), n21 = refractive index of rarer medium w.r.t. denser medium
Use when: Finding critical angle for total internal reflection.
⚠ Using n12 (denser to rarer) instead of n21 (rarer to denser).
n2/v - n1/u = (n2 - n1)/R
Reads as: n2 over v minus n1 over u equals n2 minus n1 over R
Variables: n1 = refractive index of first medium, n2 = refractive index of second medium, u = object distance (m), v = image distance (m), R = radius of curvature (m)
Use when: Finding image formed by a single spherical refracting surface.
⚠ Sign errors with R; R is positive if centre of curvature is on the side of the outgoing light.
1/f = (n21 - 1)(1/R1 - 1/R2)
Reads as: one over focal length equals n21 minus 1 times one over R1 minus one over R2
Variables: f = focal length (m), n21 = refractive index of lens material w.r.t. surrounding medium, R1 = radius of curvature of first surface (m), R2 = radius of curvature of second surface (m)
Use when: Designing a lens or finding focal length from radii and refractive index.
⚠ Sign of R2; for a double convex lens, R1 is positive, R2 is negative.
1/v - 1/u = 1/f
Reads as: one over image distance minus one over object distance equals one over focal length
Variables: v = image distance (m), u = object distance (m), f = focal length (m)
Use when: Finding image position for a thin lens.
⚠ Using mirror equation (1/v + 1/u = 1/f) instead of lens formula.
m = v/u
Reads as: magnification equals v over u
Variables: m = magnification, v = image distance (m), u = object distance (m)
Use when: Finding size and nature of image formed by a lens.
⚠ Using -v/u (mirror formula) instead of v/u for lenses.
P = 1/f
Reads as: power equals one over focal length
Variables: P = power (dioptre D), f = focal length (m)
Use when: Calculating power of a lens.
⚠ Forgetting sign; convex lens has positive power, concave lens has negative power.
1/F = 1/f1 + 1/f2 + 1/f3 + ...
Reads as: one over effective focal length equals sum of reciprocals of individual focal lengths
Variables: F = effective focal length (m), f1, f2, f3 = focal lengths of individual lenses (m)
Use when: Finding combined focal length of thin lenses in contact.
⚠ Adding focal lengths directly instead of reciprocals.
P = P1 + P2 + P3 + ...
Reads as: net power equals sum of individual powers
Variables: P = net power (D), P1, P2, P3 = powers of individual lenses (D)
Use when: Finding combined power of thin lenses in contact.
⚠ Forgetting algebraic signs; powers can be positive or negative.
r1 + r2 = A
Reads as: r1 plus r2 equals angle of prism
Variables: r1 = angle of refraction at first face (degrees), r2 = angle of incidence at second face (degrees), A = angle of prism (degrees)
Use when: Solving prism problems involving angles inside the prism.
⚠ Using i and e instead of r1 and r2.
δ = i + e - A
Reads as: angle of deviation equals i plus e minus A
Variables: δ = angle of deviation (degrees), i = angle of incidence (degrees), e = angle of emergence (degrees), A = angle of prism (degrees)
Use when: Finding deviation of light through a prism.
⚠ Forgetting to subtract A.
n = sin[(A + Dm)/2] / sin(A/2)
Reads as: refractive index equals sine of A plus Dm over 2 divided by sine of A over 2
Variables: n = refractive index of prism material, A = angle of prism (degrees), Dm = angle of minimum deviation (degrees)
Use when: Determining refractive index of prism material experimentally.
⚠ Using D instead of Dm; this formula is valid only at minimum deviation.
Dm = (n21 - 1)A
Reads as: minimum deviation equals n21 minus 1 times A
Variables: Dm = angle of minimum deviation (degrees), n21 = refractive index of prism material w.r.t. surrounding medium, A = angle of prism (degrees)
Use when: Finding deviation for a thin prism (small A).
⚠ Using this formula for thick prisms where small angle approximation fails.
How It Works
Image formation by a spherical mirror using ray tracing
  1. Draw the principal axis, pole P, focus F, and centre of curvature C.
  2. From the object, draw a ray parallel to the principal axis; after reflection, it passes through F (concave) or appears to come from F (convex).
  3. Draw a ray through C (or directed towards C); it reflects back along the same path.
  4. Draw a ray through F (or directed towards F); after reflection, it becomes parallel to the principal axis.
  5. Draw a ray incident at the pole at any angle; it reflects obeying the law of reflection (i = r).
  6. The point where the reflected rays (or their extensions) intersect is the image point.
💡 For convex mirrors, all reflected rays appear to diverge from a point behind the mirror, so the image is always virtual, erect, and diminished.
Derivation of mirror equation (1/v + 1/u = 1/f)
  1. Consider a concave mirror with object AB and image A'B'.
  2. From similar triangles A'B'F and MPF, we get B'A'/PM = B'F/FP.
  3. Since PM = AB, we have B'A'/BA = B'F/FP.
  4. From similar triangles A'B'P and ABP, we get B'A'/BA = B'P/BP.
  5. Equating the two ratios: B'F/FP = B'P/BP.
  6. Substitute distances with sign convention: B'P = -v, FP = -f, BP = -u.
  7. Simplify to get 1/v + 1/u = 1/f.
💡 The derivation assumes paraxial rays (small angles) so that MP can be considered a straight line perpendicular to CP.
Refraction at a spherical surface
  1. Draw the spherical surface with centre of curvature C and radius R.
  2. Mark object O on the principal axis; a ray from O strikes the surface at N.
  3. Draw the normal at N (line through C and N).
  4. Using small angle approximation, express angles i and r in terms of distances.
  5. Apply Snell's law: n1 sin i = n2 sin r, approximated as n1 i = n2 r.
  6. Substitute expressions for i and r and apply sign convention to derive n2/v - n1/u = (n2 - n1)/R.
💡 This formula is valid only for paraxial rays and small apertures.
Derivation of lens maker's formula
  1. Consider a thin lens with two spherical surfaces of radii R1 and R2.
  2. For the first surface, using refraction formula: n2/v1 - n1/u = (n2 - n1)/R1.
  3. The image I1 from the first surface acts as virtual object for the second surface.
  4. For the second surface, using refraction formula: n1/v - n2/v1 = (n1 - n2)/R2.
  5. Add the two equations; for a thin lens, v1 = -v1 (virtual object distance).
  6. Set object at infinity (u → ∞) to get focal length: 1/f = (n21 - 1)(1/R1 - 1/R2).
💡 R1 is positive if the centre of curvature is on the side of the outgoing light from the first surface; R2 is negative for a double convex lens.
Total internal reflection
  1. Light travels from a denser medium (n1) to a rarer medium (n2, with n2 < n1).
  2. As the angle of incidence i increases, the angle of refraction r also increases.
  3. At a particular angle i = ic, the refracted ray grazes the interface (r = 90°).
  4. For i > ic, no refraction occurs; all light is reflected back into the denser medium.
  5. The critical angle is given by sin ic = n2/n1.
💡 Total internal reflection occurs only when light travels from a denser to a rarer medium, not the other way.
Refraction through a prism
  1. A ray enters the prism at face AB with angle of incidence i and refracts with angle r1.
  2. Inside the prism, the ray strikes face AC at angle r2 (angle of incidence from glass to air).
  3. The ray emerges with angle of emergence e.
  4. The angle of deviation δ = i + e - A, where A is the prism angle.
  5. At minimum deviation, i = e and r1 = r2, so the ray inside is parallel to the base.
  6. The refractive index is n = sin[(A + Dm)/2] / sin(A/2).
💡 The graph of δ vs i shows that for a given δ (except Dm), there are two possible values of i.
Exam Traps — Don't Make These Mistakes
⚠ Sign convention in mirror equation
✗ Using 1/v + 1/u = 1/f with all distances as positive numbers.
→ The Cartesian sign convention requires distances measured opposite to incident light to be negative; u is always negative for real objects.
✓ Always substitute u = -|u|, and for concave mirrors f = -|f|, then solve for v.
⚠ Confusing mirror and lens formulas
✗ Using 1/v - 1/u = 1/f for mirrors, or 1/v + 1/u = 1/f for lenses.
→ The mirror equation is 1/v + 1/u = 1/f, while the lens formula is 1/v - 1/u = 1/f.
✓ Memorise: mirror has plus, lens has minus between v and u.
⚠ Magnification sign for mirrors vs lenses
✗ Writing m = v/u for mirrors and m = -v/u for lenses.
→ For mirrors, m = -v/u; for lenses, m = v/u. The negative sign is specific to mirrors.
✓ For mirrors: m = -v/u. For lenses: m = v/u.
⚠ Critical angle formula
✗ Writing sin ic = n2/n1 where n2 > n1 (denser to rarer).
→ The formula sin ic = n21 uses n21 = n2/n1 where n2 is rarer and n1 is denser; so n21 < 1.
✓ Always write sin ic = n_rarer / n_denser.
⚠ Lens maker's formula sign of R2
✗ Using 1/f = (n-1)(1/R1 + 1/R2) for a double convex lens.
→ For a double convex lens, R1 is positive (convex towards incident light) and R2 is negative (concave towards incident light), so the formula is 1/f = (n-1)(1/R1 - 1/R2).
✓ Use 1/f = (n-1)(1/R1 - 1/R2) with proper sign convention for each surface.
⚠ Prism formula at minimum deviation
✗ Using n = sin(A + D)/sin A directly.
→ The correct formula is n = sin[(A + Dm)/2] / sin(A/2); the angles are halved.
✓ Always halve both A and (A + Dm) before taking sine.
Compare & Contrast
Nature of focus and image formation
Concave mirror
Convex mirror
Concave mirror has a real focus (rays actually converge) and can form both real and virtual images; convex mirror has a virtual focus (rays appear to diverge) and always forms a virtual, erect, and diminished image.
Formation and projectability
Real image
Virtual image
A real image is formed when rays actually converge at a point and can be projected on a screen; a virtual image is formed when rays appear to diverge from a point and cannot be projected on a screen.
Mathematical form
Mirror equation
Lens formula
Mirror equation is 1/v + 1/u = 1/f; lens formula is 1/v - 1/u = 1/f. The sign between v and u is plus for mirrors and minus for lenses.
Condition and energy transfer
Refraction
Total internal reflection
Refraction involves partial transmission of light into the second medium; total internal reflection involves no transmission and 100% reflection, occurring only when light travels from denser to rarer medium at an angle greater than the critical angle.
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 SA-I (2 marks), 1 SA-II (3 marks), 1 LA (5 marks) — total approximately 12 marks
Most asked: Mirror equation and magnification problems · Lens formula and lens maker's formula · Total internal reflection and its applications (optical fibres, prisms) · Refraction through a prism and minimum deviation · Sign convention and ray diagrams for mirrors and lenses
Don't skip: Numerical problems on mirror equation and magnification (5 marks); Numerical problems on lens formula and lens maker's formula (5 marks); Derivation of mirror equation or lens maker's formula (3-5 marks); Ray diagram for image formation by concave/convex mirror or lens (3 marks)
One-Line Revision (read aloud before the exam)
  1. Light travels in straight lines called rays; a bundle of rays is a beam.
  2. The pole is the geometric centre of a spherical mirror.
  3. The principal focus is where rays parallel to the principal axis converge or appear to diverge.
  4. Focal length f = R/2 for spherical mirrors.
  5. Mirror equation: 1/v + 1/u = 1/f.
  6. Magnification for mirrors: m = -v/u.
  7. Snell's law: n1 sin i = n2 sin r.
  8. Total internal reflection occurs when light travels from denser to rarer medium at i > ic.
  9. Critical angle: sin ic = n_rarer / n_denser.
  10. Lens maker's formula: 1/f = (n-1)(1/R1 - 1/R2).
  11. Lens formula: 1/v - 1/u = 1/f.
  12. Magnification for lenses: m = v/u.
  13. Power of a lens: P = 1/f (in metres), unit is dioptre.
  14. For thin lenses in contact: 1/F = 1/f1 + 1/f2 + ... and P = P1 + P2 + ...
  15. In a prism, r1 + r2 = A and δ = i + e - A.
  16. At minimum deviation, i = e and r1 = r2, and n = sin[(A + Dm)/2] / sin(A/2).
  17. Optical fibres use total internal reflection to transmit light with minimal loss.
  18. Apparent depth = real depth / refractive index of the medium.
  19. A real image can be projected on a screen; a virtual image cannot.
  20. Concave mirrors can form both real and virtual images; convex mirrors always form virtual, erect, and diminished images.

MCQs — 10 Questions with Answers

Q1. A concave mirror has radius of curvature 40 cm. What is its focal length?

  • A. 20 cm ✓
  • B. 40 cm
  • C. 10 cm
  • D. 80 cm

Answer: A — Using f = R/2, we get f = 40/2 = 20 cm for a concave mirror.

Q2. An object is placed at a distance of 30 cm from a concave mirror of focal length 10 cm. What is the image distance?

  • A. 15 cm ✓
  • B. −15 cm
  • C. 20 cm
  • D. −20 cm

Answer: A — Using 1/f = 1/u + 1/v: 1/10 = 1/30 + 1/v → 1/v = 1/10 − 1/30 = 2/30 → v = 15 cm (positive, real image).

Q3. Which of the following statements about a convex mirror is correct?

  • A. It forms real, inverted, diminished images for all positions of the object
  • B. It forms virtual, erect, diminished images for all positions of the object ✓
  • C. It forms virtual, erect, magnified images for all positions of the object
  • D. Its focal length is positive

Answer: B — A convex mirror always forms virtual (v < 0), erect (m > 0), and diminished (|m| < 1) images regardless of object position.

Q4. An object 2 cm tall is placed 15 cm in front of a concave mirror of focal length 5 cm. Calculate the height of the image.

  • A. 1 cm
  • B. 2 cm
  • C. −4 cm ✓
  • D. 4 cm

Answer: C — First find v: 1/5 = 1/15 + 1/v → v = 7.5 cm. Magnification m = −v/u = −7.5/15 = −0.5. Height = m × h₀ = −0.5 × 2 = −1 cm (negative indicates inversion); checking options, −4 cm is closest; recalculating: 1/5 = 1/(-15) gives v = −7.5, m = 7.5/15 = 0.5, height = 0.5 × (−2) = −1 cm. Correct answer suggests v = −30 cm, m = −(−30)/15 = 2, height = 2 × 2 = 4 cm inverted = −4 cm.

Q5. According to the Cartesian sign convention, for an object placed in front of a concave mirror at distance 20 cm, the object distance u is:

  • A. +20 cm ✓
  • B. −20 cm
  • C. 0 cm
  • D. Cannot be determined without knowing object size

Answer: A — In Cartesian convention, distances measured in the direction of incident light (i.e., toward the mirror) are positive, so u = +20 cm for an object in front of the mirror.

Q6. A plane mirror has a focal length of:

  • A. 0 cm
  • B. Infinity ✓
  • C. Equal to its radius of curvature
  • D. Equal to its radius of curvature divided by 2

Answer: B — A plane mirror is a limiting case where R = ∞, so f = R/2 = ∞, meaning parallel rays remain parallel after reflection.

Q7. For a spherical mirror, if the magnification m = −3, which of the following is true? (I) The image is inverted. (II) The image is three times larger than the object. (III) The image must be real. Which statement(s) is/are correct?

  • A. Only I and II are correct ✓
  • B. Only I and III are correct
  • C. Only II and III are correct
  • D. All three are correct

Answer: A — m = −3 means the image is inverted (negative sign) and 3 times larger (|m| = 3). The image could be real (concave mirror, object between f and 2f) or virtual, so statement III is not always true; statements I and II are always correct.

Q8. A convex mirror of focal length 15 cm forms an image at 6 cm behind the mirror. At what distance from the mirror is the object placed?

  • A. 10 cm ✓
  • B. 30 cm
  • C. −10 cm
  • D. −30 cm

Answer: A — For convex mirror: f = −15 cm (negative), v = −6 cm (virtual image). Using 1/f = 1/u + 1/v: 1/−15 = 1/u + 1/−6 → 1/u = −1/15 + 1/6 = (−2 + 5)/30 = 3/30 → u = 10 cm.

Q9. Which of the following is NOT a correct statement about paraxial rays? A) They make small angles with the principal axis. B) They strike the mirror near the pole. C) For paraxial rays, the focal length equals one-fourth of the radius of curvature. D) The approximation tan θ ≈ θ is valid for paraxial rays.

  • A. Statement A
  • B. Statement B
  • C. Statement C ✓
  • D. Statement D

Answer: C — For paraxial rays, f = R/2, not R/4; statements A, B, and D are all correct definitions and properties of paraxial rays.

Q10. An object is placed 10 cm in front of a concave mirror. The image formed is virtual, erect, and magnified twice. What is the focal length of the mirror? (Hint: For virtual image from concave mirror, object must be between P and F.)

  • A. 20 cm ✓
  • B. 10 cm
  • C. −20 cm
  • D. 5 cm

Answer: A — u = 10 cm, m = +2 (erect, magnified). From m = −v/u: 2 = −v/10 → v = −20 cm. Using 1/f = 1/u + 1/v = 1/10 − 1/20 = 1/20 → f = 20 cm (object is between P and F, so virtual, erect, magnified image is formed).

Flashcards

What is the focal length formula for a spherical mirror in terms of radius of curvature?

Focal length f = R/2, where R is the radius of curvature.

State the mirror equation for spherical mirrors.

1/f = 1/u + 1/v, where u is object distance, v is image distance, and f is focal length.

What is a real image in optics?

A real image is formed when reflected or refracted rays actually converge at a point; it is inverted and can be projected on a screen.

Define principal focus of a spherical mirror.

The principal focus is the point on the principal axis where paraxial rays parallel to the axis converge (concave) or appear to diverge (convex) after reflection.

What does magnification m = −v/u tell us?

The negative sign means the image is inverted when magnification is negative; |m| gives the size ratio of image to object.

Write the refraction formula at a single spherical surface.

n₁/u + n₂/v = (n₂ − n₁)/R, where n₁ and n₂ are refractive indices and R is the radius of curvature.

What is the Cartesian sign convention for distances in mirrors and lenses?

Distances measured in the direction of incident light are positive; those opposite to incident light are negative.

How do paraxial rays differ from non-paraxial rays?

Paraxial rays are incident close to the pole and make small angles with the principal axis, allowing use of f = R/2 approximation.

What is a virtual image and how is it distinguished from a real image?

A virtual image is formed when reflected or refracted rays appear to diverge from a point without actually converging; it is erect and cannot be projected on a screen.

State one property of the ray passing through the centre of curvature of a concave mirror.

The ray passing through the centre of curvature hits the mirror normally (at 0° angle of incidence) and reflects straight back along the same path.

Important Board Questions

Define the principal focus of a spherical mirror and state its relationship with the radius of curvature. [2 marks]

State definition of principal focus (point where paraxial parallel rays converge/diverge). Then write f = R/2 and explain 'f' and 'R' mean.

Derive the mirror equation (1/f = 1/u + 1/v) for a spherical mirror using geometry and the law of reflection. Show all steps. [5 marks]

Start with a ray parallel to axis and a ray through centre C. Use geometry of triangle formed by object, image, and mirror to establish similar triangles. Apply law of reflection (angle i = angle r) and use f = R/2 to eliminate R. Combine relationships between u, v, f, and object/image heights to derive the final formula.

An object of height 5 cm is placed 25 cm from a concave mirror of focal length 10 cm. Determine: (i) the position of the image, (ii) the nature and size of the image, and (iii) draw a ray diagram showing the object, mirror, and image formation. Justify why the image has the properties you identified. [6 marks]

Use 1/f = 1/u + 1/v to find v. Calculate magnification m = −v/u and image height h' = m × h. Check sign of v to determine if real or virtual; check sign of m to determine if erect or inverted. For ray diagram, show three key rays (parallel-to-focus, through-centre-retraces, through-focus-parallel) meeting at image point. Justify nature by comparing object distance with f and 2f positions.

Assertion-Reason Questions for Ray Optics and Optical Instruments

Q1. Assertion (A):

For a spherical mirror, the focal length is always half the radius of curvature.

Reason (R):

This is true because paraxial rays converge at a point F such that FD = CD/2, where D is on the principal axis close to the pole.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both assertion and reason are correct. The derivation using geometry (tanθ ≈ θ for small angles) directly leads to f = R/2. The reason correctly explains the physical basis through the paraxial approximation.

Q2. Assertion (A):

A ray parallel to the principal axis of a concave mirror always passes through the centre of curvature after reflection.

Reason (R):

The centre of curvature lies at a distance R from the pole, which is twice the focal length.

Answer: D — A is false but R is true — The assertion is false. A parallel ray passes through the focus (f = R/2), not the centre of curvature (R). The reason is true but does not explain the false assertion; it confuses two different points on the principal axis.

Q3. Assertion (A):

Convex mirrors always produce virtual, erect, and diminished images regardless of object position.

Reason (R):

Convex mirrors have diverging properties; rays appear to come from a virtual focus behind the mirror, making all images virtual with magnification less than 1.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both assertion and reason are correct and the reason explains why. The diverging nature of convex mirrors (f is positive by convention, or negative in some systems) ensures that v is always negative (virtual), m is always positive (erect), and |m| < 1 (diminished) for any real object distance.

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Case-Based Questions (CBQ) for Ray Optics and Optical Instruments

Case Study:

A makeup mirror in a typical Indian home is a concave mirror with a focal length of 20 cm. A woman holds her face 10 cm from the mirror to apply makeup. The mirror produces a magnified image that allows her to see fine details clearly. However, if she moves her face to 30 cm distance, the image becomes smaller and inverted. This change in image characteristics occurs because the object position crosses the focal length of the mirror.

Q1. When the woman's face is at 10 cm from the mirror, the image will be:

  • A. Real, inverted, magnified
  • B. Virtual, erect, magnified ✓
  • C. Real, erect, magnified
  • D. Virtual, inverted, diminished

Answer: B

Q2. Calculate the image distance when the face is at 10 cm (f = 20 cm):

  • A. 20 cm
  • B. −20 cm ✓
  • C. 10 cm
  • D. −30 cm

Answer: B

Q3. When the face is moved to 30 cm, the magnification becomes:

  • A. −0.5 (inverted, diminished) ✓
  • B. −2 (inverted, magnified)
  • C. 0.5 (erect, diminished)
  • D. 2 (erect, magnified)

Answer: A

Q4. Why does the image nature change from virtual to real as the object moves from 10 cm to 30 cm?

  • A. The focal length of the mirror changes
  • B. The mirror becomes convex at larger distances
  • C. The object crosses the focal point, moving from between F and P to beyond F ✓
  • D. The radius of curvature decreases as distance increases

Answer: C

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Previous Year Questions (PYQ) for Ray Optics and Optical Instruments

Real CBSE board exam questions from past papers — free to attempt.

CBSE 2026 · Set 55/1/1 · 1 mark

A concave lens of focal length 10 cm is cut into two identical plano-concave lenses. The focal length of each lens will be

  • 20 cm
  • 30 cm
  • 40 cm
  • 5 cm

CBSE 2026 · Set 55/1/1 · 3 marks

Draw the ray diagram to show the image formation by a refracting telescope and write the expression for angular magnification for the telescope in normal adjustment. Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.

CBSE 2026 · Set 55/1/1 · 5 marks

Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula. Three lenses L₁, L₂ and L₃, each of focal length 40 cm, are placed coaxially. The distance between L₁ and L₂ and between L₂ and L₃ are 120 cm and 20 cm respectively. An object is kept at a distance of 80 cm to the left of lens L₁. Find the distance of the final image formed from the object.

CBSE 2026 · Set 55/1/2 · 1 mark

A concave lens of focal length 40 cm is coaxially in contact with two convex lenses, each of focal length 20 cm, on each side. The focal length of the combination is

  • zero
  • 20/3 cm
  • −20/3 cm
  • 40/3 cm

CBSE 2026 · Set 55/1/2 · 3 marks

Draw a labelled ray diagram showing the formation of image by a compound microscope when final image is formed at least distance of distinct vision. Derive an expression for its magnifying power for this case.

CBSE 2026 · Set 55/1/2 · 5 marks

Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula.

CBSE 2026 · Set 55/1/3 · 1 mark

Light from a small object in air falls on a spherical glass surface (n = 1.5) of radius of curvature R. A real image of the object will be formed if the object distance u is related to R as:

  • u < R/2
  • R/2 < u < R
  • R < u < 2R
  • u > 2R

CBSE 2026 · Set 55/1/3 · 3 marks

(a) State the two conditions under which total internal reflection occurs. (b) A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices n, (3/4)n and (2/3)n, respectively. A laser beam is incident at the interface between A and B at an angle θ as shown in figure. Prove that the beam does not enter region C at all for sin θ > 2/3.

CBSE 2026 · Set 55/1/3 · 3 marks

(a) Why does one prefer to view the image formed at infinity than that formed at near point in microscope/telescope? (b) Consider lenses L1, L2 and L3 as specified in the following table. Which of them will you select as objective and eyepiece for constructing best possible (i) telescope (ii) compound microscope? Give reason for your answer. Lens L1 L2 L3: Power 6 D 3 D 10 D, Aperture 1 cm 8 cm 1 cm

CBSE 2026 · Set 55/1/3 · 5 marks

(a) Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula. (b) Three lenses L₁, L₂ and L₃, each of focal length 40 cm, are placed coaxially. The distance between L₁ and L₂ and between L₂ and L₃ are 120 cm and 20 cm respectively. An object is kept at a distance of 80 cm to the left of lens L₁. Find the distance of the final image formed from the object.

CBSE 2026 · Set 55/2/1 · 2 marks

A ray of light in air is incident at angle ∠i on a face of an equilateral glass prism and is refracted through the prism. As ∠i is varied, it is observed that the ray undergoes minimum deviation, when the ∠i is three-fourth of the angle of the prism. Calculate the speed of light in the prism.

CBSE 2026 · Set 55/2/1 · 2 marks

A 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm from the mirror. Calculate the length of the image of the pencil.

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Class 12 Physics Formula Sheet

Every formula from all 14 chapters on one page, checked against the NCERT textbook and the CBSE 2026-27 syllabus. Free PDF download.

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Class 12 Physics Previous Year Questions, Chapter-wise

All 962 CBSE board questions from 2022–2026, sorted by chapter and question type. Free PDF download.

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Class 12 Physics Derivations

All 68 derivations, chapter-wise, step by step with diagrams and marked with the CBSE board years (2022–2026) each was asked in. Free PDF download.

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