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Andhra Pradesh (BIEAP)Class 10 Physical Science★ AP Board (BSEAP) SSC Physical Science · ~8 marks · Board: AP Board

Refraction of Light at Plane Surfaces

REFRACTION — why light BENDS when it changes medium. SNELL'S LAW (n₁ sin i = n₂ sin r). REFRACTIVE INDEX (n = c/v). TOTAL INTERNAL REFLECTION — the principle behind optical fibres. AP Board Class 10 Physical Science.

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By the end of this chapter you'll be able to…

1State Snell's Law and calculate refractive index; describe total internal reflection
2Distinguish convex (converging) and concave (diverging) lenses
3Draw ray diagrams for image formation by convex and concave lenses
4Apply the lens formula 1/v − 1/u = 1/f and calculate magnification
5Calculate power of a lens in dioptres; describe myopia and hypermetropia with corrections

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Why this chapter matters

Refraction of Light is one of the most formula-intensive chapters in AP SSC Physics. Snell's Law, the lens formula, magnification, and power of a lens are all tested. This chapter requires mastery of the New Cartesian sign convention and ability to handle both convex and concave lenses. Eye defects (myopia, hypermetropia) and their corrections with appropriate lenses are standard 4-mark questions. The power of a lens (P = 1/f in metres, unit = dioptre) is unique to this chapter and appears in numerical problems.

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AP Board Class 10 Physical Science: Reflection of Light, mirror formula, sign convention

Refraction of Light — Class 10 Physical Science

"Light doesn't just BOUNCE. It BENDS. When it passes from air to water, from water to glass — it changes SPEED, and therefore DIRECTION. This is REFRACTION."

1. What Is Refraction?

The BENDING of light when it passes OBLIQUELY from one TRANSPARENT medium to another. WHY does it bend? Because LIGHT CHANGES SPEED. 'Light travels FASTEST in vacuum (c = 3×10⁸ m/s). It slows down in any medium. When it enters at an ANGLE: one side of the wavefront slows down BEFORE the other → the light BENDS.'

Key Observations

Light ray, normal, and refracted ray all lie in the SAME PLANE.
Going from RARER to DENSER (air → water): light bends TOWARD the NORMAL. Angle of refraction is SMALLER.
Going from DENSER to RARER (water → air): light bends AWAY from the NORMAL. Angle of refraction is LARGER.
If light strikes PERPENDICULARLY (i = 0°): NO BENDING. r = 0°. 'Only when light strikes at an ANGLE does it refract. Normal incidence = straight through.'

2. Snell's Law: n₁ sin i = n₂ sin r

n₁ = refractive index of first medium. n₂ = refractive index of second medium.

3. Refractive Index (n): n = c/v

c = speed of light in vacuum (3×10⁸ m/s). v = speed of light in the medium. 'n is ALWAYS ≥ 1. Higher n = light travels SLOWER in that medium = MORE bending.' n for water = 1.33. n for glass = 1.5. n for diamond = 2.42 (very high — diamond sparkles because light bends so much inside it).

4. Total Internal Reflection (TIR)

Conditions

Light must travel from DENSER to RARER medium (e.g., water → air, glass → air).
Angle of incidence MUST be GREATER than the CRITICAL ANGLE (i > i_c).

Critical Angle: i_c = sin⁻¹(n₂/n₁). For water → air: i_c = sin⁻¹(1/1.33) ≈ 49°. For glass → air: i_c ≈ 42°.

Applications

Optical Fibres: Thin strands of glass. Light enters at one end. Undergoes REPEATED TIR down the fibre. Used for: INTERNET (fibre optic cables carry data as light pulses). MEDICAL ENDOSCOPY (seeing inside the body without surgery).

Mirages: On a HOT ROAD: air near the road is HOTTER (less dense, lower n) than air above. Light from the sky undergoes TIR at the boundary → reaches your eye → the road looks WET (reflecting the sky).

Diamond Sparkle: Diamond has a VERY high refractive index (2.42) → LOW critical angle (24°). Light entering a diamond undergoes MANY TIRs before emerging → BRILLIANT sparkle.

5. Common Mistakes

'Refraction always bends light' — When i = 0° (perpendicular), there is NO bending. The ray goes straight through.
'Light speeds up in denser medium' — Light SLOWS DOWN in denser medium. It's FASTEST in vacuum.
'Total internal reflection = reflection from a mirror' — TIR occurs at a BOUNDARY between media. Mirror reflection uses a COATED surface.

6. AP SSC Exam Focus

Topic	Marks
Snell's Law problems	3-4
Refractive index definition	2-3
TIR and applications	3-4
Critical angle	2-3

7. Worked Numerical Problems — Snell's Law and Refractive Index

Example 1: Light enters from air to water at an angle of incidence of 30°. If the refractive index of water is 1.33, find the angle of refraction. Solution: n₁ sin i = n₂ sin r. n_air = 1. 1 × sin 30° = 1.33 × sin r. 0.5 = 1.33 × sin r. sin r = 0.5/1.33 = 0.376. r = sin⁻¹(0.376) ≈ 22°. 'Light BENDS TOWARD the normal as it enters water.'

Example 2: The speed of light in a medium is 2 × 10⁸ m/s. Find the refractive index of the medium. (c = 3 × 10⁸ m/s) Solution: n = c/v = (3 × 10⁸)/(2 × 10⁸) = 1.5. The medium is likely GLASS (n ≈ 1.5).

Example 3: If the refractive index of diamond is 2.42, find the speed of light in diamond. Solution: n = c/v → v = c/n = (3 × 10⁸)/2.42 = 1.24 × 10⁸ m/s. 'Light travels at HALF the speed in diamond compared to vacuum — that's why diamond has such HIGH dispersive power.'

Example 4: Light passes from glass (n = 1.5) into water (n = 1.33). The angle of incidence in glass is 25°. Find the angle of refraction in water. Solution: n₁ sin i = n₂ sin r. 1.5 × sin 25° = 1.33 × sin r. 1.5 × 0.423 = 1.33 × sin r. 0.634 = 1.33 × sin r. sin r = 0.634/1.33 = 0.477. r = sin⁻¹(0.477) ≈ 28.5°. 'Since r > i, light bends AWAY from the normal — going from denser to rarer.'

8. Refraction Through a Glass Slab

Lateral Displacement: When light passes through a PARALLEL-SIDED glass slab: the EMERGENT ray is PARALLEL to the INCIDENT ray — but SHIFTED sideways. This shift is called LATERAL DISPLACEMENT (d).

Factors affecting Lateral Displacement: (1) Thickness of slab (t) — more thickness = more displacement. (2) Refractive index of glass (n) — higher n = more bending = more displacement. (3) Angle of incidence (i) — displacement changes with angle.

Verification of Snell's Law: 'A glass slab experiment is used to VERIFY Snell's law. Measure i and r at the FIRST surface. Measure e (emergence angle) and r' at the SECOND surface. You should find: i = e (for parallel sides) and r = r'.'

Lateral Displacement Formula: d = t × sin(i−r) / cos r. 'You don't need to MEMORISE the formula — but understand that d ∝ t and d ∝ sin(i−r).'

9. Lenses — Convex and Concave

	Convex Lens (Converging)	Concave Lens (Diverging)
Shape	THICKER in middle	THINNER in middle
Effect on parallel rays	CONVERGES to focus	DIVERGES (appears to come from focus)
Focal length sign	POSITIVE (+)	NEGATIVE (−)
Image types	Real or virtual	ALWAYS virtual, erect, diminished

Lens Formula: 1/f = 1/v − 1/u

Magnification: m = v/u = h'/h

'Note the DIFFERENCE from mirror formula: mirror has 1/f = 1/u + 1/v. Lens has 1/f = 1/v − 1/u. The sign of u is NEGATIVE (same as mirrors — object in front). f is POSITIVE for convex, NEGATIVE for concave.'

Power of a Lens: P = 1/f (in metres)

Unit: DIOPTRE (D). 1 D = 1 m⁻¹. Convex lens → P is POSITIVE. Concave lens → P is NEGATIVE. 'Power tells you HOW STRONG the lens is — higher |P| means more bending. A lens with f = 20 cm has P = 1/0.2 = 5 D. A lens with f = −50 cm has P = −2 D.'

Ray Diagrams for Convex Lens (6 Cases)

Object Position	Image Position	Size	Nature
At infinity	At F	Point-sized	REAL, inverted
Beyond 2F	Between F and 2F	Diminished	REAL, inverted
At 2F	At 2F	Same size	REAL, inverted
Between F and 2F	Beyond 2F	Magnified	REAL, inverted
At F	At infinity	Highly magnified	REAL, inverted
Between F and O	On SAME side as object	Magnified	VIRTUAL, erect

Ray Diagrams for Concave Lens (Always the Same)

Image is ALWAYS: VIRTUAL, ERECT, DIMINISHED, between F and O on the same side as the object.

10. Worked Numerical Problems — Lenses

Example 5: An object is placed 30 cm from a convex lens of focal length 20 cm. Find the image position and magnification. Solution: u = −30 cm, f = +20 cm. 1/f = 1/v − 1/u → 1/v = 1/f + 1/u = 1/20 + 1/(−30) = 1/20 − 1/30 = (3−2)/60 = 1/60. v = +60 cm. m = v/u = 60/(−30) = −2. 'Image is REAL (v positive for a lens means real), INVERTED (m negative), MAGNIFIED (2×), at 60 cm on the other side of the lens.'

Example 6: A concave lens of focal length 15 cm has an object placed 30 cm from it. Find the image position. Solution: u = −30 cm, f = −15 cm. 1/f = 1/v − 1/u → 1/v = 1/f + 1/u = 1/(−15) + 1/(−30) = −1/15 − 1/30 = (−2−1)/30 = −3/30 = −1/10. v = −10 cm. m = v/u = (−10)/(−30) = +1/3. 'Image is VIRTUAL (v negative), ERECT (m positive), DIMINISHED (|m| = 1/3), on the SAME side as the object — exactly as expected for a concave lens.'

Example 7: A convex lens produces a real image at 40 cm when the object is at 20 cm. Find the focal length. Solution: u = −20 cm, v = +40 cm (real → v positive). 1/f = 1/v − 1/u = 1/40 − 1/(−20) = 1/40 + 1/20 = 1/40 + 2/40 = 3/40. f = 40/3 ≈ 13.33 cm.

11. Self-Test

Q1: Light enters from air to glass (n = 1.5) at an angle of incidence of 45°. Calculate the angle of refraction. A1: n₁ sin i = n₂ sin r. 1 × sin 45° = 1.5 × sin r. 0.707 = 1.5 × sin r. sin r = 0.707/1.5 = 0.471. r = sin⁻¹(0.471) ≈ 28.1°.

Q2: What is the difference between the mirror formula and the lens formula? A2: Mirror formula: 1/f = 1/u + 1/v. Lens formula: 1/f = 1/v − 1/u. In both, u is NEGATIVE. In the mirror formula, f is negative for concave and positive for convex. In the lens formula, f is positive for convex and negative for concave.

Q3: An object is placed at 2F of a convex lens. Where is the image formed? What are its characteristics? A3: Image is formed at 2F on the OTHER side. Characteristics: REAL, INVERTED, SAME SIZE (m = −1).

Q4: Calculate the power of a convex lens of focal length 25 cm. A4: f = 25 cm = 0.25 m. P = 1/f = 1/0.25 = +4 D. Positive because it's a convex (converging) lens.

Q5: A ray of light passes through a glass slab. Why is the emergent ray parallel to the incident ray? A5: The light bends TOWARD the normal when entering glass (rarer→denser) and AWAY from the normal when exiting (denser→rarer). Since the two surfaces are PARALLEL, the NET bending is ZERO — the emergent ray is parallel but LATERALLY DISPLACED.

Q6: Why do diamond and glass sparkle? A6: Diamond has a very HIGH refractive index (2.42) → LOW critical angle (~24°) → light entering the diamond undergoes TOTAL INTERNAL REFLECTION multiple times before emerging → intense SPARKLE. Glass has lower n (~1.5) → higher critical angle (~42°) → less TIR → less sparkle.

Q7: What is the critical angle for a glass-air interface if n_glass = 1.5? A7: i_c = sin⁻¹(n₂/n₁) = sin⁻¹(1/1.5) = sin⁻¹(0.667) ≈ 41.8°. Total internal reflection occurs when i > 41.8°.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Refraction and Lens Formulas

SNELL'S LAW: n₁ sinθ₁ = n₂ sinθ₂. REFRACTIVE INDEX: n = sinI/sinR = c/v (speed in vacuum/speed in medium). LENS FORMULA: 1/v − 1/u = 1/f. MAGNIFICATION (lens): m = v/u. POWER: P = 1/f (f in metres). Unit: Dioptre (D). Positive P = converging (convex). Negative P = diverging (concave). COMBINED LENSES: P_total = P₁ + P₂. SIGN CONVENTION (Lenses): Object always to left → u is NEGATIVE. Convex lens: f is POSITIVE. Concave lens: f is NEGATIVE. EYE DEFECTS: Myopia (near-sighted) — image forms BEFORE retina. Correction: CONCAVE lens (negative power). Hypermetropia (far-sighted) — image forms BEHIND retina. Correction: CONVEX lens (positive power).

LENS FORMULA vs MIRROR FORMULA: Lens: 1/v − 1/u = 1/f (note: MINUS sign between 1/v and 1/u). Mirror: 1/v + 1/u = 1/f (PLUS sign). Students often confuse these. In lens formula, u is always negative (object on left); v can be positive (real image, right side) or negative (virtual image, same side as object). TOTAL INTERNAL REFLECTION: When light passes from denser to rarer medium at angle > critical angle, it is TOTALLY REFLECTED. Critical angle sinC = 1/n. Applications: optical fibres, diamonds sparkle, mirages.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Using the mirror formula for lenses (1/v + 1/u = 1/f)

✓ For LENSES: 1/v − 1/u = 1/f (MINUS between 1/v and 1/u). For MIRRORS: 1/v + 1/u = 1/f (PLUS between 1/v and 1/u). The difference arises from the sign convention. For lenses, with u always negative, the formula gives the correct result. Also: for lenses, magnification m = v/u (positive for erect images when both v and u are same sign). For mirrors, m = −v/u.

Practice problems

Work through this chapter's problems as a readiness check — reveal each solution, mark yourself honestly, and get your gap report at the end.

Readiness check

Are you exam-ready for Refraction of Light at Plane Surfaces?

1 problems from this chapter. Try each one, reveal the worked solution, mark yourself honestly — get your gap report at the end.

1 questions~2 min

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Refraction: bending of light when it passes from one medium to another due to a change in speed. Light bends toward normal when entering denser medium (water, glass) and away from normal when entering rarer medium (air).
•Snell's Law: n₁ sin θ₁ = n₂ sin θ₂. Refractive index n = speed of light in vacuum / speed of light in medium = c/v.
•LENS formula: 1/v − 1/u = 1/f (NOTE: MINUS sign, unlike mirror formula which has PLUS).
•Convex lens: f is POSITIVE. Concave lens: f is NEGATIVE (in New Cartesian Convention).
•Power of lens: P = 1/f (where f is in metres). Unit: DIOPTRE (D). Positive power = converging (convex). Negative power = diverging (concave).
•Magnification for lens: m = v/u (NO negative sign for lens formula, unlike mirror). Positive m = erect, negative m = inverted.
•Myopia (short-sightedness): eye lens too converging, image forms in front of retina. Corrected by CONCAVE lens (negative power).
•Hypermetropia (long-sightedness): eye lens too weak, image forms behind retina. Corrected by CONVEX lens (positive power).
•Presbyopia (age-related): eye lens loses flexibility. Corrected by bifocal lenses (both convex and concave zones).
•Total internal reflection: occurs when light travels from denser to rarer medium and angle of incidence exceeds the critical angle. Used in optical fibres, diamonds.

Andhra Pradesh (BIEAP) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Prescription glasses and contact lenses

Every spectacle or contact lens prescription worldwide uses the power formula P = 1/f in dioptres — directly from this chapter. An optometrist measuring −2.5 D means a concave lens with f = −0.4 m correcting myopia. Billions of people globally wear corrective lenses; understanding the physics of why they work requires exactly the refraction and power concepts from this chapter.

Optical fibre internet and telecommunications

India's BharatNet project is laying optical fibre to every gram panchayat — using total internal reflection to send data at the speed of light through glass fibres. Andhra Pradesh's Digital Andhra initiative depends on this infrastructure. The physics of total internal reflection (light bouncing inside glass at angles beyond the critical angle) is the foundation of the entire internet's long-distance communication.

Camera lenses and photography

Every camera (phone camera, DSLR, telescope, microscope) uses converging lenses described by the lens formula from this chapter. The autofocus mechanism adjusts the image distance v by moving the lens, maintaining v/u = constant (magnification) while keeping the image sharp. Understanding how f, u, and v relate is fundamental to optical design.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

LENS formula sign: write 1/v − 1/u = 1/f at the start of every lens problem to commit to the correct formula. The minus sign is the most common error.

Power and focal length unit: if f is given in cm, convert to metres before calculating P = 1/f. If f = 20 cm = 0.20 m, then P = +5 D.

Eye defect correction: the standard question format is 'A person cannot see objects beyond X metres. What power of lens is needed?' The answer is P = −1/X (in metres), negative (concave). For near-point problems (hypermetropia), P = 1/near-point in metres (positive, convex).

Magnification for lens: m = v/u (positive = erect, negative = inverted). Also m = image height/object height. Two ways to calculate — use whichever matches the given data.

Distinguish clearly between refraction by prism (dispersion) and refraction by lens — prism questions ask about VIBGYOR; lens questions ask about image formation. Do not mix the two.

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

STRETCH

Research chromatic aberration in lenses — different colours of light have different refractive indices in glass (red refracts least, violet most), so they focus at slightly different points. This blurs images with coloured fringes. Achromatic doublets (two lenses of different glass types cemented together) correct this — used in all quality camera lenses.

STRETCH

Investigate mirage formation — in a hot desert, air near the ground is heated and becomes less dense than air above. Light from the sky is refracted progressively away from the normal as it enters hotter air layers, eventually undergoing total internal reflection and reaching the observer's eye from below — appearing as a water pool on the ground.

STRETCH

Explore GRIN (Gradient Index) lenses — materials where the refractive index varies continuously from centre to edge. The human eye lens is a natural GRIN lens. GRIN fibres are used in endoscopes. Research how varying refractive index can replace the curved surface of a conventional lens.

STRETCH

Research the physics of fibre optic cables: how dispersion limits data rates (different wavelengths travel at slightly different speeds, causing signal pulses to spread), and how erbium-doped fibre amplifiers (EDFA) amplify signals every 80 km without converting to electrical signals — keeping light as light.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

AP Board SSC (Class 10)High — lens formula calculation and eye defect correction are standard questions worth 6–8 marks

JEE Main / Advanced (Physics)Very High — Ray Optics (lenses, mirrors, prisms, optical instruments) is one of the highest-weight chapters in Class 12 Physics

NEET (Physics section)High — optics and the human eye are tested in Class 12 Physics component of NEET

AP EAMCET (Engineering)High — refraction, lens formula, and eye defects are core Class 12 Physics topics in EAMCET

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Questions students ask

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MIRROR formula: 1/f = 1/v + 1/u (PLUS sign). LENS formula: 1/f = 1/v − 1/u (MINUS sign). The sign in the middle is the most common confusion. Additionally, magnification for mirror is m = −v/u (negative sign), while for lens it is m = v/u (no negative sign). Also, sign convention is applied differently: for mirrors, distances in front of mirror are negative; for lenses, distances on the same side as the object are negative.

In myopia, the eye is too strong (too converging) — the image of a distant object focuses in front of the retina. A concave lens DIVERGES light before it enters the eye, effectively making parallel rays (from infinity) appear to come from a closer point. This pushes the image formation point backward onto the retina. The power of the corrective lens = −1/(far point in metres). For example, if the far point is 2 m, the lens needed is P = −1/2 = −0.5 D.

The refractive index n = c/v, where c = speed of light in vacuum (3×10⁸ m/s) and v = speed of light in glass. Glass has n ≈ 1.5 means light travels at 2×10⁸ m/s in glass — about 67% of its vacuum speed. Light slows because photons interact with the glass molecules — they are absorbed and re-emitted repeatedly as they pass through. Different types of glass (crown glass, flint glass) have different refractive indices (1.52 vs 1.62) because of different molecular compositions.

When light travels from denser (glass) to rarer (air) medium, if the angle of incidence exceeds the critical angle (for glass-air: ~42°), NO light is refracted — ALL light is reflected internally. This is total internal reflection. In optical fibres, light is fed into a thin glass fibre and hits the glass-air boundary at angles greater than the critical angle — it bounces along the fibre by repeated total internal reflection with virtually zero loss. This allows light to carry internet data, phone calls, and medical imaging (endoscope) signals over thousands of kilometres with minimal attenuation.

Diamond has a very HIGH refractive index (n ≈ 2.42) and correspondingly LOW critical angle (~24°). This means total internal reflection occurs at almost any angle of incidence. The diamond is cut precisely so that light entering it undergoes multiple total internal reflections before exiting — it 'traps' light and then releases it explosively in multiple directions. Additionally, the high refractive index creates strong dispersion (splitting of white light into colours), producing the rainbow flashes. Glass (n ≈ 1.5) has critical angle ~42° and less dispersion — far less sparkle.

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