Chapter 1 · Let us assessTextbook pages 22–24

Let Us Assess, Q1–Q6 – Solutions വിലയിരുത്താം

The first six end-of-chapter questions: reading a ray diagram (Fig 1.26), completing a water–glass figure (Fig 1.27), a ray that bends away from the normal, the refractive-index table (Table 1.5), comparing two media (Fig 1.28) and spotting total internal reflection (Fig 1.29). Try each one in your science diary first, then step through the solution.

📖 What you need (pages 5–7 and 10 of this guide)

Question 1 · Which medium is denser? (Fig 1.26)

1. A, B എന്നീ മാധ്യമങ്ങളിലൂടെ പ്രകാശരശ്മി കടന്നുപോകുന്ന രേഖാചിത്രം നല്കിയിരിക്കുന്നു. The diagram shows a ray of light passing through two media A and B (Fig 1.26).

a) A, B എന്നീ മാധ്യമങ്ങളിൽ ഏത് മാധ്യമത്തിലായിരിക്കും പ്രകാശവേഗം കുറവ്?
b) ഇവയിൽ പ്രകാശിക സാന്ദ്രത കൂടിയ മാധ്യമം ഏതായിരിക്കും? ഉത്തരം സാധൂകരിക്കുക.
  1. In which of the media A and B will the speed of light be less?
  2. Which of them is the optically denser medium? Justify your answer.

Look carefully: the boundary between A and B is a vertical line, so the normal at the point of incidence is a horizontal line. Compare the angle the ray makes with that horizontal normal in A and in B.

🎬 Solution animation – Fig 1.26 (redrawn)
Answer: The interface is vertical, so the normal at the point of incidence is horizontal. In A the ray makes a large angle (about 45°) with this normal; in B it makes a much smaller angle (about 20°) – the ray is closer to the normal in B. So on entering B the ray bends towards the normal: it has gone from a rarer to a denser medium.
(a) The speed of light is less in B.
(b) B is the optically denser medium – a ray passing obliquely from a rarer to a denser medium bends towards the normal, and that is what happens when it enters B.
⚠️ Common trap

Measuring the angles from the surface (the vertical line). In B the ray looks “flatter”, i.e. it is nearer the horizontal normal, not nearer the surface. Always draw the normal first – here it is horizontal – and then compare the angles with it.

Question 2 · Complete the figure (Fig 1.27)

2. താഴെ കൊടുത്തിരിക്കുന്ന ചിത്രം പൂർത്തിയാക്കുക. പതനകോൺ, അപവർത്തനകോൺ ഇവ അടയാളപ്പെടുത്തുക. Complete the figure given below (Fig 1.27: a ray in water falls obliquely on a water–glass interface). Mark the angle of incidence and the angle of refraction.

Which is optically denser, water or glass? (Table 1.2: water 1.33, glass 1.5.) Going from rarer to denser, the ray bends towards the normal – so the refracted ray in glass is steeper than the incident ray, but it still goes on to the right.

🎬 Solution animation – completing Fig 1.27
🧪 Try it – draw the refracted ray yourself

Drag the first slider to place your refracted ray (amber, dashed), then check it. The correct ray is drawn with water n = 1.33 and glass n = 1.5. Change i and watch: r is always a little smaller than i (except at i = 0°, where both are 0°).

Answer: Water is optically rarer and glass optically denser, so the ray passing obliquely from water into glass bends towards the normal. Draw the refracted ray in the glass, on the other side of the normal, steeper than the incident ray (closer to the dashed normal).
i = the angle between the incident ray and the normal (in water); r = the angle between the refracted ray and the normal (in glass); r < i.
🚀 Go further – how steep exactly? (not in your textbook)

Snell's law, n₁ sin i = n₂ sin r, gives the exact angle: 1.33 × sin 60° = 1.5 × sin r ⇒ sin r = 0.768 ⇒ r ≈ 50°. So a 60° ray in water becomes about 50° in glass – it turns by only about 10°, because water and glass are not very different in optical density.

⚠️ Common trap

Drawing the refracted ray on the same side of the normal as the incident ray, or bending it the wrong way. The ray keeps going forward (across the normal) – only its slope changes.

Question 3 · X to Y, r greater than i

3. പ്രകാശം മാധ്യമം X ൽ നിന്ന് മാധ്യമം Y യിലേക്ക് കടന്നു പോകുന്നു. ഇവിടെ പതന കോണിനേക്കാൾ കൂടുതലാണ് അപവർത്തനകോൺ. Light passes from medium X into medium Y. Here the angle of refraction is greater than the angle of incidence.

a) X, Y ഇവയിൽ ഏതു മാധ്യമത്തിൽ ആയിരിക്കും പ്രകാശത്തിന് വേഗം കൂടുതൽ?
b) അപവർത്തനാങ്കം കൂടിയ മാധ്യമം ഏതായിരിക്കും?
c) പ്രകാശപാത ചിത്രീകരിക്കുക.
  1. In which of X and Y will light have the greater speed?
  2. Which medium has the higher refractive index?
  3. Draw the path of light.

r > i means the refracted ray is further from the normal than the incident ray – the ray bent away from the normal. When does that happen?

🎬 Solution animation – the ray bends away
Answer: r > i, so the ray bends away from the normal: it has gone from an optically denser medium (X) to an optically rarer medium (Y).
(a) Light is faster in Y (the rarer medium).
(b) X has the higher refractive index (n = c/v: slower speed ⇒ higher n).
(c) Diagram: draw the interface and the normal; the incident ray in X makes angle i with the normal; the refracted ray in Y, on the other side of the normal, makes a larger angle r with it (bent away from the normal).
💡 Why this matters

This is exactly what happens to light leaving a temple pond or an aquarium (water → air): it bends away from the normal, and so the bottom looks raised – the pond looks shallower than it really is. Be careful when you step in!

Question 4 · Table 1.5 – refractive indices

4. വിവിധ മാധ്യമങ്ങളുടെ അപവർത്തനാങ്കം പട്ടികയിൽ കൊടുത്തിരിക്കുന്നു. The refractive indices of different media are given in the table.

Medium മാധ്യമംRefractive index അപവർത്തനാങ്കം
crown glass ക്രൗൺ ഗ്ലാസ്1.52
glycerine ഗ്ലിസറിൻ1.47
sunflower oil സൺഫ്ളവർ ഓയിൽ1.47
water ജലം1.33
flint glass ഫ്ളിന്റ് ഗ്ലാസ്1.62

Table 1.5

a) പ്രകാശം ഏതു മാധ്യമത്തിലൂടെയാണ് ഏറ്റവും കൂടിയ വേഗത്തിൽ സഞ്ചരിക്കുന്നതെന്ന് കണ്ടെത്തുക.
b) ഗ്ലിസറിനിൽ നിന്ന് സൺഫ്ളവർ ഓയിലിലേക്ക് ചരിഞ്ഞ് പതിക്കുന്ന പ്രകാശരശ്മിയുടെ ദിശയ്ക്ക് വ്യതിയാനം സംഭവിക്കുമോ? കാരണം വിശദമാക്കുക.
c) ഗ്ലാസിൽ നിന്ന് പട്ടികയിൽ സൂചിപ്പിച്ച ഓരോ മാധ്യമത്തിലേക്കും പ്രകാശം കടത്തിവിടുന്നു. 30° പതനകോണിലാണ് പ്രകാശം പതിപ്പിക്കുന്നതെങ്കിൽ ഏതു മാധ്യമത്തിലായിരിക്കും അപവർത്തനകോൺ ഏറ്റവും കൂടുതൽ? എന്തുകൊണ്ട്?
  1. Find the medium through which light travels with the highest speed.
  2. Will a ray falling obliquely from glycerine into sunflower oil change direction? Explain the reason.
  3. Light is sent from glass into each medium in the table. If it falls at an angle of incidence of 30°, in which medium will the angle of refraction be the greatest? Why?

n = c/v, so the lowest n means the highest speed. Two media with the same n have the same optical density. In (c) the ray leaves crown glass (1.52): the lower the n of the second medium, the bigger the drop in optical density and the more the ray bends away from the normal.

🎬 Solution animation – reading Table 1.5
🧪 Try it – crown glass → each medium (live angle read-outs)

Keep i = 30°: water gives the largest angle of refraction, flint glass the smallest (it is denser than crown glass, so the ray bends towards the normal). Push i above about 61° and the ray cannot get into water at all – total internal reflection!

Answer:
(a) Water – it has the lowest refractive index (1.33). Since n = c/v, the lowest n means the highest speed of light.
(b) No change of direction. Glycerine and sunflower oil have the same refractive index (1.47), so they have the same optical density and light has the same speed in both. With no change of speed at the interface, the ray goes straight on.
(c) In water. Light goes from crown glass (1.52) into each medium. Water has the lowest refractive index, so the drop in optical density (glass → water) is the largest; the ray bends furthest away from the normal and the angle of refraction is the greatest. (Into flint glass, 1.62, which is denser than crown glass, the ray bends towards the normal and the angle of refraction is less than 30°.)
🚀 Go further – the actual angles (Snell's law, not in your textbook)

1.52 × sin 30° = n₂ × sin r gives: water r ≈ 34.8°, glycerine and sunflower oil r ≈ 31.1°, crown glass 30.0° (no change), flint glass r ≈ 28.0°. The order agrees with the qualitative answer: lowest n → largest r.

💡 Why this matters

A clean glass rod dipped in a liquid with the same refractive index almost disappears – no bending, no reflection, so there is nothing to see at its edges. Jewellers and gem testers use this trick with special liquids.

Question 5 · Medium 1 or medium 2? (Fig 1.28)

5. ചിത്രം നിരീക്ഷിക്കുക. രണ്ടു വ്യത്യസ്ത മാധ്യമങ്ങളിൽ പ്രകാശരശ്മി പതിക്കുന്നതു ചിത്രീകരിച്ചിരിക്കുന്നു. Observe the figure (Fig 1.28). A ray of light falling on two different media is shown: from air at 40° into medium 1 (angle of refraction 20°) and into medium 2 (angle of refraction 30°).

a) ഏതു മാധ്യമത്തിനാണ് പ്രകാശികസാന്ദ്രത കൂടുതൽ? എന്തുകൊണ്ട്?
b) ഏതു മാധ്യമത്തിന്റെ അപവർത്തനാങ്കമാണ് കൂടുതൽ?
  1. Which medium has the higher optical density? Why?
  2. Which medium has the higher refractive index?

The angle of incidence is the same (40°) in both. In which medium does the ray bend more towards the normal – the one with r = 20° or r = 30°?

🎬 Solution animation – Fig 1.28 (redrawn)
Answer: In both cases the ray goes from air (rarer) into the medium and bends towards the normal. For the same angle of incidence (40°), the angle of refraction is smaller in medium 1 (20°) than in medium 2 (30°): the ray bends more towards the normal in medium 1.
(a) Medium 1 has the higher optical density – the more the ray bends towards the normal, the more the light is slowed down, i.e. the denser the medium.
(b) Medium 1 has the higher refractive index (higher optical density ⇔ lower speed ⇔ higher n).
🚀 Go further – estimate the indices (Snell's law)

With n(air) = 1: n₁ = sin 40° / sin 20° ≈ 0.643 / 0.342 ≈ 1.88; n₂ = sin 40° / sin 30° ≈ 0.643 / 0.5 ≈ 1.29. Medium 1 is denser than glass; medium 2 is a little rarer than water.

⚠️ Common trap

“30° is bigger, so medium 2 bends more.” No – a bigger angle of refraction means the ray stayed closer to its old direction (less bending). Compare each r with i = 40°: medium 1 turned the ray by 20°, medium 2 by only 10°.

Question 6 · Reflection or refraction? (Fig 1.29)

6. ചിത്രം നിരീക്ഷിക്കുക.
a) പൂർണ്ണാന്തര പ്രതിപതനം സൂചിപ്പിക്കുന്ന ചിത്രം ഏതാണ്?
b) അപവർത്തനത്തെ സൂചിപ്പിക്കുന്ന ചിത്രങ്ങൾ ഏതൊക്കെയാണ്? Observe the figures (Fig 1.29 (a), (b), (c)).

  1. Which figure shows total internal reflection?
  2. Which figures show refraction?

In which figure does the light come back out on the same side it entered, turned round by the inside faces? In which figures does the light go through and bend at the faces?

🎬 Solution animation – Fig 1.29 (redrawn)
🗂️ Sorter – tap the figure(s) that fit
Score: 0 / 0
(a) Total internal reflection → Fig 1.29 (a). The light enters the right-angled prism normally (no bending), meets the slanting inside face at 45° – greater than the critical angle of glass (42°) – and is totally reflected; the same happens at the second face, so the light comes back out parallel to the way it came (this is how a reflector works).
(b) Refraction → Fig 1.29 (b) and (c). In the glass slab ABCD the ray bends towards the normal at Q (air → glass) and away from it at R (glass → air). In the triangular prism ABC the ray bends at Q and again at R (at both faces).
💡 Why this matters

The red reflector on the back of your bicycle or a KSRTC bus has no bulb and no battery. It is a sheet of tiny right-angled prisms like Fig 1.29 (a): headlight beams from the vehicles behind are sent straight back to their drivers by total internal reflection.

Check yourself

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