The Human Eye and the Colourful World - Defects of vision and their correction, dispersion of light through a glass prism, and atmospheric refraction phenomena

Hello students! Welcome to one of the most beautiful and fascinating chapters in Class 10 Physics: The Human Eye and the Colourful World. Have you ever wondered why the sky looks blue, how rainbows appear after rain, or why some of your classmates need glasses to read the blackboard?

In this tutorial, we will break down these exciting phenomena step-by-step using simple logic, neat explanations, and clear concepts directly aligned with your NCERT syllabus.

1. Defects of Vision and Their Correction

Our eye has a remarkable ability to adjust its focal length so we can see both nearby and far-off objects clearly. This ability is called the Power of Accommodation. However, due to aging, strain, or structural changes in the eyeball, our vision can develop defects. Let's study the three major vision defects.

A. Myopia (Nearsightedness)

• What happens? A myopic person can see nearby objects clearly, but distant objects appear blurry.
• Where does the image form? The image of a distant object is formed in front of the retina, rather than on the retina itself.
• Far Point: The far point of a myopic eye is closer than infinity.
• Causes:
  1. Excessive curvature of the eye lens (lens becomes too thick/converging).
  2. Elongation of the eyeball.
• Correction:
  • Corrected using a Concave Lens (diverging lens) of suitable power.
  • The concave lens slightly diverges incoming parallel rays so that after passing through the eye lens, they focus exactly on the retina.

B. Hypermetropia (Farsightedness)

• What happens? A hypermetropic person can see distant objects clearly, but nearby objects appear blurry.
• Where does the image form? The image of a nearby object is formed behind the retina.
• Near Point: The near point of the hypermetropic eye moves farther away than $25\text{ cm}$.
• Causes:
  1. Focal length of the eye lens is too long (lens becomes too thin/weak).
  2. Eyeball has become too small.
• Correction:
  • Corrected using a Convex Lens (converging lens) of suitable power.
  • The convex lens provides the extra converging power needed to bring the focus point back forward onto the retina.

C. Presbyopia (Old-Age Farsightedness)

• What happens? With aging, it becomes difficult to read comfortably and distinctly without corrective glasses.
• Causes: Gradual weakening of the ciliary muscles and diminishing flexibility of the crystalline eye lens.
• Correction:
  • Corrected using a Convex Lens of suitable power for reading.
  • If a person suffers from both myopia and hypermetropia, they require Bifocal Lenses.
  • A bifocal lens consists of both concave (upper portion for distance vision) and convex (lower portion for near vision) lenses.

2. Refraction and Dispersion of Light Through a Glass Prism

Now, let's leave the human eye and step into the world of light refraction!

Refraction Through a Glass Prism

Unlike a rectangular glass slab (where opposite faces are parallel), a triangular glass prism has two inclined plane surfaces.

• When a ray of light passes through a prism, it bends towards the normal when entering glass (denser medium) and bends away from the normal when exiting into air (rarer medium).
• Because of the inclined faces, the emergent ray bends at an angle to the direction of the incident ray. This angle is called the Angle of Deviation ($\angle D$).

    Incident Ray ---> [ Prism ] ---> Emergent Ray
                          \
                           └---> Angle of Deviation (D)

Dispersion of White Light

When sunlight (white light) passes through a glass prism, it splits into a band of seven colors. This phenomenon is called Dispersion.

• Spectrum: The band of colored components produced is called a spectrum: VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red).
• Why does this happen?
  • White light is a mixture of light rays of different wavelengths.
  • Different colors travel at different speeds in glass.
  • Red light deviates the least (longest wavelength, highest speed in glass).
  • Violet light deviates the most (shortest wavelength, lowest speed in glass).

Recombination of White Light

Isaac Newton proved that white light consists of seven colors by placing two identical prisms side-by-side: one in an upright position and the second in an inverted position.

1. The first prism splits white light into seven colors.
2. The second inverted prism recombines all seven colors back into a beam of white light.

Rainbow Formation

A rainbow is a natural spectrum appearing in the sky after a rain shower. It is produced by the dispersion of sunlight by tiny water droplets suspended in the atmosphere.

Step-by-step formation:

1. Refraction & Dispersion: Sunlight enters a spherical raindrop, refracts, and splits into constituent colors.
2. Internal Reflection: The split light hits the back inner surface of the raindrop and gets internally reflected.
3. Refraction: The light refracts again as it exits the raindrop into the air, reaching the observer's eye as a vivid rainbow.

💡 Teacher's Tip: Remember the sequence of events inside a raindrop for your exams: Refraction & Dispersion $\rightarrow$ Internal Reflection $\rightarrow$ Refraction.

3. Atmospheric Refraction Phenomena

Earth’s atmosphere is not uniformly dense. Hot air is lighter (rarer) than cool air (denser). As light passes through layers of air with continuously changing optical densities, it bends continuously. This is called Atmospheric Refraction.

      Star Light (Space)
             │
             ▼   [Upper Atmosphere - Optically Rarer]
             ░
             ░   [Lower Atmosphere - Optically Denser]
             ▼
        Observer's Eye

A. Twinkling of Stars

1. Stars are very far away, so they act as point sources of light.
2. As star light enters Earth's atmosphere, it undergoes continuous refraction through layers of varying air density and temperature.
3. The continuous shifting of the atmosphere causes:
   • The apparent position of the star to fluctuate slightly.
   • The amount of light entering the eye to flicker continuously.
4. Hence, the star appears to twinkle.

Why don't planets twinkle?

Planets are much closer to Earth and act as extended sources (a collection of many point sources of light). The total variation in light coming from all point sources averages out to zero, neutralizing the twinkling effect!

B. Advanced Sunrise and Delayed Sunset

Have you noticed that we can see the Sun about 2 minutes before the actual sunrise and 2 minutes after the actual sunset?

• Mechanism: When the Sun is slightly below the horizon, light coming from it travels from rarer atmospheric layers to denser layers near Earth's surface.
• Result: The light rays continuously bend downwards towards the normal. To an observer on Earth, the Sun appears slightly raised above the actual horizon.
• Total time added to daylight = $2\text{ mins (sunrise)} + 2\text{ mins (sunset)} = \mathbf{4\text{ minutes}}$.

Practice Questions with Solutions

Let's test your understanding with 3 essential NCERT-style questions!

Question 1 (Numerical on Vision Defect)

A person with a myopic eye cannot see objects beyond $1.2\text{ m}$ distinctly. What should be the type and power of the lens used to restore proper vision?

Solution:

• For a myopic eye, the object at infinity ($u = -\infty$) must form a virtual image at the person's far point ($v = -1.2\text{ m}$).

• Using the Lens Formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ $\frac{1}{f} = \frac{1}{-1.2} - \frac{1}{-\infty}$ $\frac{1}{f} = -\frac{1}{1.2} \implies f = -1.2\text{ m}$

• Calculating Power ($P$): $P = \frac{1}{f\text{ (in meters)}} = \frac{1}{-1.2} = -0.83\text{ D}$

Answer: A concave lens of focal length $-1.2\text{ m}$ and power $-0.83\text{ D}$ is required.

Question 2 (Conceptual Physics)

Explain why a glass prism splits white light into a spectrum, whereas a rectangular glass slab does not produce dispersion.

Solution:

1. Glass Prism: The two refracting faces of a triangular glass prism are inclined at an angle to each other. When white light passes through, different colors refract at different angles of deviation, causing them to spread out into a spectrum upon exiting.
2. Glass Slab: A rectangular glass slab has parallel refracting surfaces. The deviation produced at the first face is equal and opposite to the deviation produced at the second face.
3. Therefore, all colors recombine inside the slab, and the emergent ray is simply displaced laterally (parallel to the incident ray) without splitting into a spectrum.

Question 3 (Atmospheric Refraction)

Why does the Sun appear reddish during sunrise and sunset, but white at noon?

Solution:

1. At Sunrise and Sunset: Light from the Sun has to travel through a longer distance in the Earth's atmosphere.
   • Shorter wavelengths (blue and violet) are scattered away by atmospheric particles long before reaching our eyes.
   • Only the longer wavelengths (red and orange light) pass through unscattered and reach our eyes, making the Sun look reddish.
2. At Noon: The Sun is directly overhead, so light travels a much shorter distance through the atmosphere.
   • Very little blue and violet light gets scattered.
   • Hence, all colors reach our eyes almost equally, making the Sun appear white.

Summary Checklist for Revision

• Myopia: Image in front of retina $\rightarrow$ Corrected with Concave lens.
• Hypermetropia: Image behind retina $\rightarrow$ Corrected with Convex lens.
• Dispersion: Splitting of light into VIBGYOR (Red deviates least, Violet most).
• Rainbow: Refraction $\rightarrow$ Internal Reflection $\rightarrow$ Refraction.
• Atmospheric Refraction: Causes twinkling of stars & 2-minute advanced sunrise / delayed sunset.

Keep practicing ray diagrams, and you will score full marks in this chapter! Good luck with your studies!