Model Test – Solved ഉത്തരങ്ങൾ
Every question of the model paper, in the same order, with the full answer, the marking scheme, an animated ray diagram or working for every diagram and numerical question, and a link to the page where the idea is taught. Try each one again before you open the answer, and mark your own paper honestly.
Rays are red with arrows; the normal (ലംബം) is a dashed line drawn at the point of incidence; every angle is measured from the normal. Media are coloured as in the textbook: air grey, water blue, glass green. The angles in the animations are worked out with the real law of refraction, so they are drawn to scale.
💡 n = c/v – what is n called?
Refractive index (അപവർത്തനാങ്കം) n = c/v, where c = 3 × 108 m/s is the speed of light in vacuum (ശൂന്യത) and v its speed in the medium.
Marking: 1 mark.
📖 Review this on Page 6 · Refractive index
💡 In which medium is light slowest?
Light is slowest in diamond (1.25 × 108 m/s in Table 1.1), so diamond is the optically densest (പ്രകാശികസാന്ദ്രത കൂടിയ മാധ്യമം). Order: air < water < glass < diamond.
Marking: 1 mark for (d).
📖 Review this on Page 5 · Table 1.1 and optical density
💡 It must be greater than – not equal to – the critical angle.
Total internal reflection (പൂർണ്ണാന്തര പ്രതിപതനം) needs an angle of incidence greater than the critical angle. Only 50° is greater than 42°. At exactly 42° the ray grazes along the surface (r = 90°).
Marking: 1 mark for (d).
📖 Review this on Page 10 · Critical angle · Page 14 · Let us assess Q7
💡 Angles are measured from the normal. Where is the ray?
A ray falling along the normal (ലംബമായി പതിക്കുന്ന) has i = 0°; it goes straight on, r = 0° – it is not deviated.
Marking: 1 mark.
📖 Review this on Page 7 · Rule (iv)
💡 Is water → air rarer → denser or denser → rarer?
Rarer → denser: towards the normal; denser → rarer: away from the normal (ലംബത്തിൽ നിന്ന് അകലുന്നു).
Marking: 1 mark.
📖 Review this on Page 7 · Table 1.3
💡 Light from a star passes through many layers of air.
The layers of the atmosphere keep changing in temperature and pressure, so their optical density keeps changing. Starlight is refracted irregularly, and the apparent position and brightness of the star keep changing – it twinkles.
Marking: 1 mark (“refraction” alone: ½ mark).
📖 Review this on Page 9 · Twinkling stars
💡 What is (m/s) ÷ (m/s)?
n = c/v is speed ÷ speed: the units m/s cancel. Refractive index is a pure number (glass 1.5).
Marking: 1 mark for (d).
📖 Review this on Page 6 · Key box 4 · Page 3 · Ratios have no unit
💡 The textbook side box on p. 20.
Charles K. Kao showed that very pure glass fibres (ഒപ്റ്റിക്കൽ ഫൈബർ) could carry light signals over long distances – the basis of today’s internet cables.
Marking: 1 mark.
📖 Review this on Page 11 · Optical fibres
💡 Divide c by v; the powers of ten cancel.
Given: v = 2.04 × 108 m/s; c = 3 × 108 m/s
Formula: n = c/v
Substitution: n = (3 × 108) ÷ (2.04 × 108) = 3 ÷ 2.04
Answer: n ≈ 1.47 (no unit)
The 108 cancels; the answer matches glycerine in Table 1.5.
Marking: ½ for the formula, ½ for substitution, 1 for the answer (writing a unit: lose ½).
📖 Review this on Page 6 · n = c/v · Page 3 · Dividing powers of ten
💡 Rarer → denser: towards or away from the normal?
(a) Draw the normal at the point of incidence. Air → water is rarer → denser, so the refracted ray in the water bends towards the normal. Mark i between the incident ray and the normal (in air) and r between the refracted ray and the normal (in water).
(b) i is greater than r (for i = 45°, r is about 32°).
Marking: 1 mark for the correct refracted ray with the normal, ½ for marking i and r from the normal, ½ for (b).
📖 Review this on Page 7 · Towards the normal · Page 2 · Measure from the normal
💡 Which way must the light travel, and how big must the angle be?
(1) Light must travel from an optically denser medium to an optically rarer medium (for example glass → air).
(2) The angle of incidence must be greater than the critical angle (ക്രിട്ടിക്കൽ കോൺ) of the pair of media (42° for glass–air).
Marking: 1 mark for each condition.
📖 Review this on Page 10 · Key box 6, Fig 1.18
💡 Where does the light from the fish bend, and which way?
Light from the fish passes from water (denser) into air (rarer) and bends away from the normal at the surface. The boy’s eye traces the ray back in a straight line, so he sees the fish at a raised position, higher than where it really is. So he must aim below the image he sees.
Marking: 1 mark for “bends away from the normal at the water surface”, 1 mark for “the fish appears higher than its real position”.
📖 Review this on Page 8 · Coin, pond and fishing
💡 Think of Table 1.4 in the textbook.
| Reflection from a plane mirror സമതല ദർപ്പണം | Total internal reflection പൂർണ്ണാന്തര പ്രതിപതനം |
|---|---|
| Light is not totally reflected – some is absorbed | Light is totally reflected |
| Happens at any angle of incidence | Happens only when the angle of incidence is greater than the critical angle |
| Light may come from any medium onto the mirror | Happens only when light goes from a denser to a rarer medium |
Marking: 1 mark for each correct difference (Table 1.4).
📖 Review this on Page 11 · Table 1.4
| Medium | P | Q | R |
|---|---|---|---|
| Speed of light (m/s) | 2.25 × 108 | 1.25 × 108 | 2 × 108 |
💡 Lower speed = higher refractive index = optically denser.
Given: v(Q) = 1.25 × 108 m/s; c = 3 × 108 m/s
Formula: n = c/v
Substitution: (a) n = 3 ÷ 1.25
Answer: (a) n(Q) = 2.4
(b) Light is slowest in Q, so Q is optically the densest (it is like diamond).
(c) n(R) = 3/2 = 1.5 and n(P) = 3/2.25 ≈ 1.33. Light is faster in P, so R → P is denser → rarer: the ray bends away from the normal.
Marking: 1 mark for each part; in (c) ½ for the answer, ½ for the reason.
📖 Review this on Page 6 · Table 1.2 · Page 5 · Optical density · Page 7 · The rules
💡 Compare each angle with 42°.
(a) At i = 42° the refracted ray goes along the surface – the angle of refraction is 90°. This angle of incidence is the critical angle of glass.
(b) At 50° (greater than 42°) the ray is not refracted; it is reflected completely back into the glass at 50° – total internal reflection.
(c) The light goes from glass (denser) to air (rarer), so it bends away from the normal: r (60°) is greater than i (35°).
Marking: 1 mark for each part.
📖 Review this on Page 10 · Fig 1.17 critical-angle lab
💡 Two surfaces – two refractions.
(a) At Q (air → glass) and at R, where the ray leaves the slab (glass → air).
(b) At Q it bends towards the normal (about 31° inside the glass); at R it bends away from the normal and leaves along RS.
(c) The emergent ray RS is parallel to the incident ray PQ, but shifted sideways.
Marking: 1 mark for each part; in (b) normals must be drawn at both surfaces.
📖 Review this on Page 8 · Glass slab, Fig 1.9
💡 Which air is optically rarer – hot or cool?
(a) A mirage (മരീചിക).
(b) The air near the hot road is hotter and optically rarer; the layers above are cooler and denser. Light from the sky or a distant tree travelling down passes from denser to rarer layers and bends away from the normal more and more. Near the road the angle of incidence becomes greater than the critical angle, and the light is totally internally reflected upwards into our eyes.
(c) The light from the top of the tree arrives at the eye from lower down than the light from the bottom, so the image appears inverted, below the road – just like a reflection in a pool of water.
Marking: ½ for (a), 2 marks for (b) (rarer hot air ½, bending away ½, total internal reflection 1), ½ for (c).
📖 Review this on Page 11 · Mirage · Page 15 · Mirage lab
| Medium | water | kerosene | crown glass | diamond |
|---|---|---|---|---|
| Refractive index | 1.33 | 1.44 | 1.52 | 2.42 |
💡 Higher n → slower light → smaller critical angle.
(a) Water – it has the lowest refractive index, and v = c/n.
Given: n = 2.42; c = 3 × 108 m/s
Formula: v = c/n
Substitution: v = (3 × 108) ÷ 2.42
Answer: (b) v ≈ 1.24 × 108 m/s
(c) Kerosene (1.44) is denser than water (1.33): denser → rarer, so it bends away from the normal. (Kerosene floats on water – it has a lower mass density – but it is optically denser.)
(d) Diamond. Its critical angle (24.4°) is much smaller, so light inside it meets the faces at angles greater than the critical angle far more often. It is totally internally reflected many times and comes out through the top towards our eyes.
Marking: (a) 1, (b) 1 (formula ½, answer with unit ½), (c) 1 (½ answer, ½ reason), (d) 2 (1 for diamond, 1 for the reason).
📖 Review this on Page 14 · Let us assess Q9 · Page 10 · Critical angle · Page 15 · Sparkle lab
💡 Light falling along the normal is not refracted; compare 45° with 42°.
(a) The ray enters PQ along the normal (no refraction), strikes the first slanted face at A at 45°, is reflected to the second face at B, again at 45°, is reflected again and leaves through PQ.
(b) The light goes from glass to air (denser → rarer) and 45° is greater than the critical angle 42°, so it is totally internally reflected.
(c) It leaves parallel to the incoming light, going back towards the source – the headlights of the vehicle behind – so its driver sees the cycle at night without any bulb.
(d) Each prism turns the light through 90° (one total internal reflection at the hypotenuse).
(e) No. The light would meet the slanted face at 45°, which is less than the critical angle of water (48.6°). It would refract out instead of being totally reflected, and the image would be very dim.
Marking: (a) 2 (path 1, angles 1), (b) 1, (c) ½ + ½ for the use, (d) ½, (e) ½ with the reason. Total 5.
📖 Review this on Page 11 · Reflector and periscope · Page 15 · Reflector and periscope labs · Page 13 · Let us assess Q6
Marks summary
| Section | Questions | Marks each | Total | Topics |
|---|---|---|---|---|
| A | 1–8 | 1 | 8 | refractive index, optical density, critical angle, normal incidence, towards/away, twinkling stars, unit of n, Charles K. Kao |
| B | 9–13 | 2 | 10 | n = c/v, ray diagram air → water, conditions for total internal reflection, fishing (apparent position), mirror vs total internal reflection |
| C | 14–17 | 3 | 12 | speeds and optical density, critical-angle experiment, glass slab ray diagram, mirage |
| D | 18–19 | 5 | 10 | refractive-index table and diamond’s sparkle, reflector and periscope prisms |
| Total | 40 | |||
- Cool-off (15 min) – read the whole paper. Mark each question that needs a ray diagram, and for each pair of media decide “rarer → denser” or “denser → rarer” before you write.
- Section A – about 10 minutes. One-word answers; no unit for refractive index.
- Section B – about 20 minutes. For Q9 write Given, Formula, Substitution, Answer. In diagrams draw the normal first.
- Section C – about 25 minutes. Use a ruler and protractor: a neat diagram with normals and arrows earns most of the marks.
- Section D – about 25 minutes. Answer every part (a)–(e); compare angles with the critical angle in words (“45° is greater than 42°”).
- Checking – keep 10 minutes: angles measured from the normal? arrows on rays? towards/away correct? 108 written in speeds?
Count your marks: 32 or more – excellent; 24–31 – good, revise the pages linked under the questions you missed; below 24 – go back through pages 5, 6, 7, 10 and 11 with their labs and do the scored quiz again. Then return to the chapter home and tick off what you have learned.