NCERT Solutions Class 10 Science Chapter 10 In-text Questions — The Human Eye and the Colourful World

NCERT Class 10 Science — The Human Eye and the Colourful World, the in-text QUESTIONS box on page 164. All 4 questions solved.

Also here. Solutions to the end-of-chapter questions for this chapter and the activities are on their own pages.

Chapter 10 pauses only once, and it does so straight after the section on defects of vision — so all four questions are about the same thing from different angles: what the eye can do by itself, where that ability runs out, and which lens takes over when it does. Two ideas carry the box:

• Accommodation — the ciliary muscles change the curvature of the eye lens, and so its focal length, to keep the image on the retina as the object moves.
• The near and far points — the closest and furthest positions an eye can focus on. For a normal eye these are 25 cm and infinity; a defect moves one of them.

Key insight. Every one of these questions turns on a single fact: the image distance in the eye cannot change. The retina is at a fixed distance behind the lens, so when the object distance changes, the focal length has to change instead. Accommodation is that adjustment, a defect is a limit on it, and a spectacle lens is what you put in front when the limit has been reached.

Questions, page 164. The box following Section 10.2, on defects of vision and their correction.

Page 164, Question 1

What is meant by power of accommodation of the eye?

Solution. The retina sits at a fixed distance behind the eye lens, so the image distance is fixed. If an object moves nearer or further, the only way to keep its image sharp on the retina is to change the focal length of the lens itself.

The eye does this with the ciliary muscles. When they relax, the lens becomes thin and its focal length long, and distant objects are in focus. When they contract, the lens thickens and its focal length shortens, bringing near objects into focus. That ability to adjust its own focal length is what is meant by the power of accommodation.

It has a limit. The lens cannot be squeezed indefinitely, so the focal length cannot fall below a certain value — which is why a normal eye cannot focus on anything nearer than about 25 cm.

Page 164, Question 2

A person with a myopic eye cannot see objects beyond 1.2 m distinctly. What should be the type of the corrective lens used to restore proper vision?

Solution. “Cannot see beyond 1.2 m” means the far point has come in from infinity to 1.2 m. A myopic eye converges light too strongly, so the image of a distant object forms in front of the retina.

The corrective lens has to undo exactly that excess convergence. A concave lens diverges the incoming light first, so that the eye’s own over-strong lens then brings it to focus on the retina rather than in front of it.

What the lens must do precisely is take an object at infinity and form its image at the person’s far point, 1.2 m in front of the eye, since that is the furthest point the eye can still focus. With $u = \infty$ and $v = -1.2$ m,

$$\frac1f = \frac1v – \frac1u = \frac{1}{-1.2} – 0 \quad\Longrightarrow\quad f = -1.2\ \text{m}$$

$$P = \frac1f = \frac{1}{-1.2\ \text{m}} \approx -0.83\ \text{D}$$

The negative focal length and negative power both confirm it: the lens is concave.

Page 164, Question 3

What is the far point and near point of the human eye with normal vision?

Solution. The two points mark the range over which accommodation works. The far point is the furthest position an eye can focus on with the ciliary muscles fully relaxed; for a normal eye that is infinity, which is why distant stars can be seen sharply.

The near point is the closest position that can still be focused, with the ciliary muscles fully contracted. For a normal adult eye it is about 25 cm — bring a book nearer than that and it blurs, however hard you try. This 25 cm is also called the least distance of distinct vision.

Page 164, Question 4

A student has difficulty reading the blackboard while sitting in the last row. What could be the defect the child is suffering from? How can it be corrected?

Solution. Read the symptom carefully: the difficulty is with a distant object, the blackboard, while the child would have no trouble with a book. Trouble with distant vision and not with near vision is myopia, or near-sightedness — the far point has moved in from infinity to somewhere inside the classroom.

The cause is that the eye converges light too strongly, either because the eye lens is too curved or because the eyeball is too long, so the image of a distant object forms in front of the retina instead of on it.

The correction is a concave lens of the right power, which diverges the light slightly before it enters the eye so that the image falls back onto the retina.

Common mistakes

• Defining accommodation as the eye changing the image distance. It cannot — the retina is fixed. What changes is the focal length of the lens, and saying so is the difference between the definition and a description of it.
• Answering Question 2 with “convex lens” because the eye needs help. The eye is already converging too strongly; adding more convergence makes it worse. The myopic eye needs divergence, so the lens is concave. Hypermetropia is the one corrected by a convex lens.
• Giving the near point as 25 m, or the far point as 25 cm. The pair is 25 cm and infinity, and it is worth fixing which is which by what they mean: the near point is where reading stops being possible, the far point is where the eye is completely relaxed.
• Taking $v = +1.2$ m in the calculation for Question 2. The image formed by the spectacle lens is virtual and on the same side as the object, so $v$ is negative. A positive $v$ would give a converging lens, which is the opposite of what is needed.
• Diagnosing the last-row student with hypermetropia. The symptom names the distance: trouble with the blackboard is trouble seeing far, so it is myopia. Hypermetropia would show up as trouble reading a book held at a normal distance.

Practise next

• The end-of-chapter Exercises for this chapter, where Questions 5, 6 and 7 put numbers on exactly this correction and ask for the power of the lens.
• Chapter 9, Light – Reflection and Refraction — its in-text questions set up the lens formula and the power of a lens that this box relies on.