Class 10 Science Chapter 10 The Human Eye and the Colourful World

Key Concept: Color Distinction

b) Different wavelengths of the rays
[Solution Description] When white light passes through a prism, it undergoes dispersion. Each color in the spectrum has a different wavelength and therefore bends by different amounts with respect to the incident ray while passing through the prism. This causes each color to emerge along a different path. Thus, the distinct paths taken due to varying wavelengths make colors appear distinct.

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Key Concept: Pupil and Eye Structure

d) Cornea
[Solution Description] The pupil is situated behind the cornea and is surrounded by the iris, which controls its size.

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Key Concept: Vision Defect Combination

d) Bifocal lens

[Solution Description] The person’s condition suggests they have both myopia (difficulty with distant vision) and hypermetropia (difficulty with close vision), possibly presbyopia. Bifocal lenses are typically used to correct dual vision defects, providing two distinct powers for distance and near vision.

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Key Concept: Cornea and Pupil

c) The cornea regulates light intensity, working together with the pupil
[Solution Description] The cornea directs light towards the pupil while also helping to refract it. The pupil then controls the amount of light entering the inner eye by expanding or contracting, thus working with the cornea to regulate the light that reaches the retina.

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Key Concept: Correction Mechanism

b) By diverging light rays to focus on the retina
[Solution Description]
In myopia, images of distant objects are focused in front of the retina. Concave lenses spread out light rays before they enter the eye, effectively moving the image back onto the retina, thus correcting the vision.

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Key Concept: Basic Concept

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Both the assertion and reason are true statements. Rayleigh scattering explains why the sky appears blue, as it scatters shorter wavelengths (like blue) much more effectively than longer wavelengths (like red). Therefore, the reason correctly explains the assertion.

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Key Concept: Vision Range

b) 25 cm to infinity
[Solution Description] A normal human eye can see clearly from a near point of about 25 cm to infinity. This range is defined by the limits of accommodation where the eye can adjust its focal length to bring objects into clear focus.

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Key Concept: Accommodation Failure

b) Blurred vision
[Solution Description] When the eye loses its power of accommodation, it becomes difficult to focus on objects at varying distances. This results in blurred vision for either nearby or faraway objects, depending on whether the defect is presbyopia, myopia, or hypermetropia.

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Key Concept: Cause and Effect

d) The image forms in front of the retina, causing blur.
[Solution Description] Myopia, or near-sightedness, is a condition where the eye focuses images in front of the retina instead of directly on it. This can occur due to excessive curvature of the eye lens or elongation of the eyeball. The focal point for distant objects falls short of the retina, causing blurred vision. Using a concave lens corrects this by diverging incoming light rays before they enter the eye, shifting the focus back onto the retina.

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Key Concept: Angle Calculation

b) 12°
[Solution Description]
The angle of deviation (D) can be calculated using the formula $D = i + e – A$, where i is the angle of incidence, e is the angle of emergence, and A is the angle of the prism. However, if not all values are provided directly, we need to use given or derived data to find D. In this problem, since only one side’s calculation is shown without emergent ray details, assume minimum deviation condition for simplicity as an estimation:

Let the refractive index (n) between air and glass be constant; hence $sin(i)/sin(r)$ remains constant.

Assuming equilateral triangle-like simple conditions:
Calculate deviation due to each face:
$D = (i – r) \times 2 = (40^\circ – 28^\circ) \times 2 = 24^\circ$

Hence, the expected deviation in this setting is approximately $12^\circ$.

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Key Concept: Comparative Analysis

c) Only in a prism, the emergent ray bends at an angle.
[Solution Description] In a rectangular glass slab, the emergent ray is parallel to the incident ray but laterally displaced. However, in a prism, the emergent ray is not parallel to the incident ray; instead, it is bent at an angle. This results from the non-parallel surfaces of the prism causing further deviation.

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Key Concept: Twinkling Cause

b) Atmospheric refraction
[Solution Description] Stars twinkle because of atmospheric refraction. As the light travels through the turbulent and continuously changing atmosphere, it gets refracted multiple times, causing fluctuations in the amount of starlight reaching our eyes, which makes the stars appear to twinkle.

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Key Concept: Sunrise Timing

a) Atmospheric refraction
[Solution Description] The Sun appears visible before the actual sunrise due to atmospheric refraction. As sunlight travels through the earth’s atmosphere, it bends downwards, allowing us to see the Sun slightly before it rises above the horizon.

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Key Concept: Angle Comparison

b) Smaller

[Solution Description]

At the first interface of the prism, light moves from air (a less dense medium) to glass (a denser medium). According to Snell’s Law, which is $n_1 \sin(\angle i) = n_2 \sin(\angle r)$, where $n_1$ and $n_2$ are the refractive indices of air and glass respectively. Since $n_2 > n_1$, it follows that $\sin(\angle r) < \sin(\angle i)$. Hence, $\angle r < \angle i$, meaning the angle of refraction is smaller than the angle of incidence. Click Here to Download Notes

Key Concept: Refraction of Light through Prism

c) Because different colors have different wavelengths
[Solution Description] Different colors of light have different wavelengths, causing them to refract differently. Shorter wavelengths (such as violet) bend more than longer wavelengths (such as red), leading to dispersion into a spectrum of colors.

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Key Concept: Light Bending

d) Red
[Solution Description] When white light passes through a prism, each color bends at a different angle. Red light bends the least because it has the longest wavelength among visible colors.

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Key Concept: Internal Reflection

b) It is internally reflected
[Solution Description] Inside a raindrop, the light undergoes internal reflection after being refracted upon entry, contributing to the formation of a rainbow.

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Key Concept: Correction Method

b) Convex lens
[Solution Description] Hypermetropia, also known as far-sightedness, is corrected by using a convex lens. A convex lens helps focus the light on the retina by providing additional converging power.

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Key Concept: Multi-Defect Comparison, Complex Cause Analysis

a) Elongation of the eyeball leading to nearsightedness
[Solution Description] Myopia chiefly affects distant vision clarity, while astigmatism distorts vision at all distances due to irregular curvature of the cornea or lens. The combined effect during low-light conditions like nighttime driving exacerbates focusing difficulties on both near and far objects.

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Key Concept: Accommodation Mechanism

a) Lens thickens, muscles contract
[Solution Description] When viewing nearby objects, the ciliary muscles contract to increase the curvature of the eye lens. This makes the lens thicker, decreasing its focal length to focus on the nearby object.

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Key Concept: Basic Definition

a) Scattering of light by colloidal particles
[Solution Description] The Tyndall effect is the scattering of light by colloidal particles, which results in making the path of a beam of light visible through a colloidal solution.

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Key Concept: Light Behavior

b) It is dispersed and internally reflected
[Solution Description]
Sunlight entering a raindrop is dispersed and internally reflected within the drop, leading to the separation of light into its constituent colors, forming a rainbow.

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Key Concept: Advanced Scattering, Mathematical Analysis

b) 5.92

[Solution Description] According to Rayleigh’s law, the intensity of scattered light is inversely proportional to the fourth power of the wavelength:

$I \propto \dfrac{1}{\lambda^4}.$

Let $\lambda_{blue} = 450$ nm and $\lambda_{red} = 700$ nm. We need to calculate the ratio of intensities of scattered blue light ($I_{blue}$) to red light ($I_{red}$):

$\dfrac{I_{blue}}{I_{red}} = \left(\dfrac{\lambda_{red}}{\lambda_{blue}}\right)^4.$

Substitute the given wavelengths:

$\dfrac{I_{blue}}{I_{red}} = \left(\dfrac{700}{450}\right)^4.$

Calculate step by step:

$\dfrac{700}{450} \approx 1.5556.$

Now raise it to the fourth power:

$1.5556^4 \approx 5.92.$

Therefore, blue light is approximately 5.92 times more effectively scattered than red light.

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Key Concept: Real-world Application

b) Rainbow

[Solution Description] A rainbow is formed when sunlight is dispersed by water droplets present in the atmosphere. Light entering the droplet is refracted, internally reflected, and then refracted again upon leaving, causing the dispersion into its constituent colors. This creates the circular arc of colors seen in a rainbow.

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Key Concept: Pupil and Iris

c) Iris
[Solution Description] The iris, which is a muscular diaphragm, controls the size of the pupil. By adjusting the diameter of the pupil, the iris regulates how much light can enter the eye. This adjustment helps in protecting the retina from excessive light or allows more light when it’s dim.

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Key Concept: Tyndall Effect Examples

d) Sunlight passing through mist

[Solution Description] The Tyndall effect is observed when light is scattered by particles in a colloid or in very fine suspensions. Among the given options, sunlight passing through mist involves the suspension of tiny water droplets in the air, which scatters light and makes the path of the light beam visible.

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Key Concept: Real-life Application

c) Red light undergoes the least amount of scattering
[Solution Description] Danger signal lights are red because red light is scattered the least by fog or smoke due to its longer wavelength. This makes it visible from a distance even under poor atmospheric conditions.

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