Mix Examples - The Human Eye and the Colourful World Questions in English

(N/A) The power of the lens is negative $(-1\, D)$,which indicates that the lens is a concave lens.
Concave lenses are used to correct myopia (nearsightedness).
Therefore,the person is suffering from myopia and is using a concave lens.

(N/A) The scattering of light depends on the size of the particles present in the atmosphere. Particles like smoke,tiny water droplets,suspended dust particles,and air molecules scatter light of different wavelengths.
In space,there is no atmosphere,which means there are no air molecules or other particles to scatter sunlight.
Since no light is scattered towards the observer's eyes in space,the sky appears dark.

(N/A) Myopia: The eyeball becomes longer than normal. Due to this,the image formed by the eye lens is focused in front of the retina.
$(b)$ Hypermetropia: The eyeball becomes shorter than normal. Due to this,the image formed by the eye lens is focused behind the retina.

(N/A) The defect of vision is Hypermetropia (farsightedness).
$(b)$ The formula for focal length $f$ in meters is given by $f = \frac{1}{P}$,where $P$ is the power in Diopters $(D)$.
Given $P = +0.5 \text{ D}$.
$f = \frac{1}{0.5} = 2 \text{ m}$.
Therefore,the focal length of the convex lens is $2 \text{ m}$.

(N/A) The pupil regulates and controls the amount of light entering the eye by adjusting its size.
The ciliary muscles control the curvature of the eye lens,which helps in the process of accommodation,allowing the eye to focus on objects at varying distances.

(N/A) The child's eye is suffering from the defect of myopia (near-sightedness).
$(b)$ This defect can be corrected by using a concave lens of suitable focal length. The concave lens diverges the incoming parallel rays from a distant object,making them appear to originate from the child's far point,thus allowing the eye lens to focus the image on the retina. The ray diagram for the correction of myopia is shown below.

(N/A) These are common defects of vision.
Hypermetropia (Farsightedness): $A$ person suffering from this defect can see distant objects clearly but cannot see nearby objects clearly. In this defect,the near point of the eye shifts farther away than $25 \ cm$.
Causes:
$1.$ The eyeball becomes too short.
$2.$ The focal length of the eye lens becomes too large.
Correction: This condition is corrected using a converging or convex lens.
Myopia (Nearsightedness): $A$ person suffering from myopia can see nearby objects clearly but cannot see distant objects clearly. In this defect,the far point of the eye comes closer than infinity.
Causes:
$1.$ The eyeball becomes too long.
$2.$ The focal length of the eye lens becomes too small.
Correction: This condition is corrected using a diverging or concave lens.

(N/A) $(i)$ Ciliary muscles: These are the muscles that hold the eye lens in position and control its curvature.
$(ii)$ Accommodation: The ability of the eye lens to adjust its focal length to focus objects at varying distances is called accommodation.
$(iii)$ Blind spot: This is the point on the retina where the optic nerve leaves the eye. There are no photoreceptor cells at this point,so any image formed here is not transmitted to the brain.

(B) We need two eyes because a human being has a horizontal field of view of about $150^{\circ}$ with one eye and about $180^{\circ}$ with two eyes. Thus,two eyes provide us with a wider horizontal field of view.
With one eye,the world looks flat,i.e.,two-dimensional. With two eyes,the view is three-dimensional,which adds the dimension of depth to our vision.

(N/A) The phenomenon of splitting of white light into its constituent seven colours when passing through a glass prism is known as the dispersion of light.
When white light passes through a prism,it disperses into the following colours in the order of increasing wavelength (from violet to red): $Violet$,$Indigo$,$Blue$,$Green$,$Yellow$,$Orange$,and $Red$ (often remembered by the acronym $VIBGYOR$).

(B) When white light passes through a prism,it splits into its constituent seven colours. This band of colours is known as a spectrum. The sequence of colours is violet,indigo,blue,green,yellow,orange,and red $(VIBGYOR)$. The phenomenon of splitting white light into its component colours is called dispersion.

(N/A) Red colour has the maximum wavelength,while violet colour has the minimum wavelength. According to the relationship between wavelength and deviation,the amount of bending (deviation) is inversely proportional to the wavelength. Since red light has the longest wavelength,it bends the least. Conversely,violet light has the shortest wavelength,so it bends the most.

(N/A) The impression of an object seen by the eye persists on the retina for $1/16$ of a second,even after the object is removed from the field of view.
If another object is seen before this time interval,the impressions of the two objects merge in the brain to give us the sensation of continuity.
This property of the human eye is known as persistence of vision.

(N/A) The four common defects of vision that can be corrected with the use of spectacles are:
$(i)$ Myopia (nearsightedness): Corrected using concave lenses.
$(ii)$ Hypermetropia (farsightedness): Corrected using convex lenses.
$(iii)$ Presbyopia: Corrected using bifocal or progressive lenses.
$(iv)$ Astigmatism: Corrected using cylindrical lenses.

(N/A) Isaac Newton was the first to use a glass prism to obtain the spectrum of sunlight. He tried to split the colours of the spectrum of white light further by using another similar prism. However,he could not get any more colours.
He then placed a second identical prism in an inverted position with respect to the first,as shown in the diagram. This allowed all the colours of the spectrum to pass through the second prism. He found a beam of white light emerging from the other side of the second prism. This observation gave Newton the idea that sunlight is made up of seven colours.

(N/A) The twinkling of a star is due to atmospheric refraction of starlight. As starlight enters the Earth's atmosphere,it undergoes continuous refraction before reaching the observer. This refraction occurs in a medium with a gradually changing refractive index. Because the atmosphere bends starlight towards the normal,the apparent position of the star is slightly different from its actual position. When viewed near the horizon,the star appears slightly higher than its actual position.
Furthermore,this apparent position is not stationary but keeps changing slightly because the physical conditions of the Earth's atmosphere are dynamic. Since stars are extremely distant,they act as point-sized sources of light. As the path of light rays from the star varies slightly,the apparent position fluctuates,and the amount of starlight entering the eye flickers. This causes the star to appear brighter at one moment and fainter at another,which is the twinkling effect.
Planets are much closer to the Earth and are seen as extended sources of light. If we consider a planet as a collection of a large number of point-sized sources,the total variation in the amount of light entering our eye from all these individual sources averages out to zero,thereby nullifying the twinkling effect.

(N/A) The Earth's atmosphere is a heterogeneous mixture of minute particles. These particles include smoke,tiny water droplets,suspended particles of dust,and molecules of air. When a beam of light strikes such fine particles,the path of the beam becomes visible. The light reaches us after being scattered by these particles. The phenomenon of scattering of light by colloidal particles is called the Tyndall effect.

(N/A) The molecules of air and other fine particles in the atmosphere have a size smaller than the wavelength of visible light.
These particles are more effective at scattering light of shorter wavelengths (at the blue end of the spectrum) than light of longer wavelengths (at the red end).
The red light has a wavelength about $1.8$ times greater than blue light.
Thus,when sunlight passes through the atmosphere,the fine particles in the air scatter the blue colour (shorter wavelengths) more strongly than the red colour.
The scattered blue light enters our eyes,making the sky appear blue.

(N/A) In the absence of an atmosphere, there is no scattering of sunlight by air molecules or dust particles. Consequently, no light reaches the observer's eye from the sky, making it appear dark.
$(b)$ According to Rayleigh scattering, the intensity of scattered light is inversely proportional to the fourth power of its wavelength $(I \propto 1/\lambda^4)$. Red light has the longest wavelength in the visible spectrum, meaning it undergoes the least scattering. This allows red light to travel longer distances without being significantly dispersed, making it clearly visible even from a distance through fog, smoke, or dust.

(B) The sky appears blue on Earth because the atmosphere contains gas molecules and particles that scatter sunlight (Rayleigh scattering).
In outer space,there is no atmosphere to scatter light.
Since there is no scattered light reaching the eyes of an astronaut,the sky appears dark and black.

(N/A) When the sun is overhead at noon,the light coming from the sun travels a relatively shorter distance through the atmosphere to reach us.
As a result,only a small portion of the blue component of the white light is scattered,while most of the light reaches the observer.
Since the light reaching us from the overhead sun contains almost all its component colours in the correct proportion,the sun appears white.

(N/A) The sky appears dark from the surface of the moon because there is no atmosphere to scatter sunlight.
$(b)$ The water molecules of the ocean scatter blue light more strongly than light of other colours due to the phenomenon of scattering. Consequently,the ocean appears bluish.

(N/A) When a person can see near objects but is unable to see distant objects clearly,the defect is known as near-sightedness (myopia). This defect is caused by either $(i)$ excessive curvature of the cornea or $(ii)$ elongation of the eyeball. As a result,the image of a distant object is formed in front of the retina instead of on the retina. It can be corrected by using a concave lens of appropriate power.
$(b)$ Astigmatism is a vision defect where a person is unable to focus equally on objects in all directions (horizontal and vertical) simultaneously. This occurs because the cornea or the eye lens has different curvatures along different planes. This defect is corrected by using cylindrical lenses.

(N/A) The student is suffering from Myopia (near-sightedness).
$(b)$ The defect is corrected by using a concave lens of appropriate power. The concave lens diverges the incoming parallel rays from a distant object so that they appear to originate from the student's far point,allowing the eye lens to focus them on the retina.
$(c)$ $A$ concave lens is used to correct this defect.

(N/A) convex lens forms a virtual and erect image when the object is placed between the optical centre $(O)$ and the principal focus $(F_1)$.
To explain this,consider two rays originating from the top of the object $(B)$: one ray moves parallel to the principal axis and passes through the focus $(F_2)$ after refraction,while the other ray passes through the optical centre $(O)$ without deviation.
When these two refracted rays are extended backwards,they appear to meet at a point $(B')$ on the same side of the lens as the object.
Thus,the image $(A'B')$ formed is virtual,erect,and magnified,and it lies on the same side as the object.

(N/A) The blue colour of the sky is due to the scattering of sunlight by the molecules of gases present in the Earth's atmosphere. According to Rayleigh's law of scattering, the intensity of scattered light is inversely proportional to the fourth power of its wavelength $(I \propto 1/\lambda^4)$. Since blue light has a shorter wavelength compared to other colours in the visible spectrum, it is scattered more strongly by the atmospheric particles. In the absence of an atmosphere, there would be no particles to scatter the sunlight. Consequently, no light would reach our eyes from the sky, and it would appear black.

(B) The difference in the colour of the sun is due to the scattering of light.
At noon,the sun is overhead,and the light travels a shorter distance through the atmosphere,resulting in less scattering,so the sun appears white.
During sunrise and sunset,the sun is near the horizon,and the light travels a longer distance through the atmosphere.
Most of the blue light and shorter wavelengths are scattered away by atmospheric particles.
Therefore,the light that reaches our eyes consists mainly of longer wavelengths (red/orange),giving the sun a reddish appearance.

(D) When white light passes through a glass prism,it undergoes dispersion because the prism offers different refractive indices for different wavelengths of light.
Since the speed of light of different colours is different in the glass medium,each colour bends (refracts) by a different angle.
Violet light has the shortest wavelength and bends the most,while red light has the longest wavelength and bends the least.
Therefore,the red light deviates the least.

(N/A) In bright sunlight,the size of the pupil is small to restrict the amount of light entering the eye. When we enter a dim room,the pupil takes some time to dilate (expand) so that more light can enter the eye,which eventually allows us to see objects clearly.

(N/A) The pupil of the eye regulates and controls the amount of light entering the eye.
In bright sunlight,the iris causes the pupil to contract,making its size small to limit light entry.
When we enter a dark cinema hall,the amount of light is significantly lower.
It takes some time for the iris to relax and the pupil to expand in size to allow more light to enter the eye so that we can see objects clearly in the dim light.

(N/A) The refraction of a light ray through a glass prism is shown in the diagram below.
Key components of the diagram:
$1$. $A$ is the apex of the prism.
$2$. $OP$ is the incident ray.
$3$. $i$ represents the angle of incidence.
$4$. $PQ$ is the refracted ray inside the prism.
$5$. $QR$ is the emergent ray.
$6$. $e$ is the angle of emergence.
$7$. $\delta$ represents the angle of deviation,which is the angle between the incident ray and the emergent ray.

(N/A) The "power of accommodation of the eye" is the ability of the eye lens to adjust its focal length to focus objects at varying distances clearly on the retina.
$(b)$ The image distance in the eye remains constant. It is equal to the distance between the eye lens and the retina, which does not change regardless of the object's distance.

(N/A) The least distance of distinct vision is the minimum distance at which an object can be placed so that a normal eye can see it clearly without any strain. For a normal adult eye,this distance is approximately $25 \ cm$.
$(b)$ When we shift our focus from a distant tree to reading a book,the ciliary muscles contract. This contraction increases the curvature of the eye lens,making it thicker. This increase in thickness increases the converging power of the lens,allowing the image of the nearby object (the book) to be focused clearly on the retina.

(N/A) The two main causes of myopia are:
$(i)$ Excessive curvature of the eye lens (decrease in focal length).
$(ii)$ Elongation of the eyeball.
In myopia,the image of a distant object is formed in front of the retina instead of on the retina itself. This defect is corrected by using a concave lens of suitable power,which diverges the incoming light rays so that the image is formed on the retina.

(N/A) $(i)$ The least distance of distinct vision for a normal eye is $25\, cm$.
$(ii)$ For a long-sighted eye (hypermetropia),the least distance of distinct vision increases. $A$ person with hypermetropia cannot see objects clearly at the normal near point $(25\, cm)$ because the image is formed behind the retina. The near point of such an eye shifts further away from the eye,meaning the minimum distance at which they can see clearly is greater than $25\, cm$. This is illustrated in the diagram where the near point $N$ is at a distance greater than $25\, cm$.

(N/A) The power of the lens is negative $(P = -2.5 \ D)$,which indicates that the person is using a concave lens.
Since a concave lens is used to correct myopia (nearsightedness),the person is suffering from myopia.
The focal length $f$ is calculated using the formula $f = 1 / P$.
Substituting the value: $f = 1 / (-2.5) = -0.4 \ m$.
Converting to centimeters: $f = -0.4 \times 100 = -40 \ cm$.
The negative sign indicates that the lens is concave.

(N/A) The image of the object formed by the eye lens is formed on the retina of the eye.
The nature of the image formed on the retina is real and inverted.
The image is converted into electrical signals by photoreceptors in the retina and is sent to the brain via the optic nerve.

(N/A) normal human eye can adjust its focal length using the ciliary muscles, a process known as accommodation.
To see distant objects, the ciliary muscles relax, making the eye lens thin and increasing its focal length.
To see near objects, the ciliary muscles contract, making the eye lens thick and decreasing its focal length.
The far point of a normal human eye is at infinity $(\infty)$.
The near point of a normal human eye is at $25\, cm$ from the eye.

(N/A) $(i)$ The person is suffering from $Presbyopia$.
$(ii)$ The person will require $Bifocal$ lenses. $Bifocal$ lenses consist of both convex and concave lenses. The upper portion consists of a concave lens to correct myopia (nearsightedness) for distant vision,and the lower portion consists of a convex lens to correct hypermetropia (farsightedness) for near vision. This combination allows the person to see both distant and nearby objects clearly.

(N/A) Dispersion of light is the phenomenon of splitting of white light into its constituent seven colours when it passes through a transparent medium like a glass prism.
$(i)$ The component of white light that deviates the least is Red light because it has the longest wavelength.
$(ii)$ The component of white light that deviates the most is Violet light because it has the shortest wavelength.

(N/A) The ciliary muscles change the curvature of the eye lens as per the requirement of the eye. This process changes the focal length of the eye lens,which is known as accommodation.
When the ciliary muscles are relaxed,the lens becomes thin,increasing its focal length,which allows the eye to see distant objects clearly.
When viewing closer objects,the ciliary muscles contract,which makes the eye lens thicker and decreases its focal length,allowing the eye to focus on near objects.
$(b)$ The far point of a normal human eye is at infinity,and the near point is at $25\, cm$ from the eye.

(N/A) The least distance of distinct vision is defined as the minimum distance at which an object can be placed so that the eye lens can form a clear and sharp image on the retina without any strain. For a normal adult eye,this distance is approximately $25 \ cm$.
$(b)$ This distance varies with age because the flexibility of the ciliary muscles and the eye lens decreases over time. In very young people,the eye lens is highly flexible,allowing for a shorter least distance of distinct vision. In contrast,as people age,the lens becomes less flexible and the ciliary muscles weaken (a condition often associated with presbyopia),which increases the least distance of distinct vision.

(N/A) The Sun is visible to us about two minutes before the actual sunrise and about two minutes after the actual sunset because of atmospheric refraction.
By actual sunrise,we mean the actual crossing of the horizon by the Sun.
As light from the Sun enters the Earth's atmosphere,it undergoes refraction due to the varying density of air layers.
This causes the light rays to bend towards the normal,making the Sun appear slightly higher than its actual position when it is just below the horizon.
The time difference between the actual sunset and the apparent sunset is about two minutes.
$(b)$ The phenomenon responsible for the apparent flattening of the Sun's disc at sunrise and sunset is also atmospheric refraction.

(N/A) $(i)$ The defect of vision represented is Hypermetropia (farsightedness).
$(ii)$ The two possible causes of this defect are:
$(a)$ The eyeball has become too short,so that light rays from a nearby object are focused at a point behind the retina.
$(b)$ The focal length of the eye lens is too long,meaning the ciliary muscles are unable to make the lens sufficiently convex to focus the image on the retina.
$(iii)$ This defect can be corrected by using a convex lens of appropriate power. The convex lens converges the incoming light rays before they enter the eye,allowing the eye lens to focus the image exactly on the retina,as shown in the diagram.

(N/A) The person is suffering from Hypermetropia (farsightedness).
Reasons for this defect:
$(a)$ The eyeball has become too short,so that light rays from a nearby object are focused at a point behind the retina.
$(b)$ The focal length of the eye lens is too long because the ciliary muscles are unable to make the lens sufficiently convex.
This defect is corrected by using a convex lens of appropriate power,which converges the light rays before they enter the eye,allowing them to focus on the retina.

(N/A) $(i)$ Hypermetropia (far-sightedness). The reason is that the image of nearby objects is focused behind the retina instead of on the retina.
$(ii)$ This defect arises due to the following two causes:
$(a)$ The focal length of the eye lens is too long.
$(b)$ The eyeball has become too small.

(N/A) $(i)$ Scattering of light: It is the phenomenon of the redirection of light in different directions by the particles (such as atoms,molecules,dust,or smoke) present in the atmosphere.
$(ii)$ Why the sky appears blue: The fine particles in the atmosphere have a size smaller than the wavelength of visible light. These particles scatter light of shorter wavelengths (like blue and violet) much more strongly than light of longer wavelengths (like red). Since blue light has a shorter wavelength,it is scattered the most,which is why the sky appears blue to our eyes.
$(iii)$ Why the sun appears reddish at sunrise: At sunrise,the sun is near the horizon. Sunlight has to travel through a much thicker layer of the atmosphere to reach the observer. During this long journey,most of the blue and shorter wavelength light is scattered away by the atmospheric particles. Only the light of longer wavelengths,such as red,reaches our eyes,which is why the sun appears reddish at sunrise.

(N/A) The Sun appears reddish at sunrise and sunset,while it appears white at noon when it is overhead.
At sunrise and sunset,the light from the Sun travels through a thicker layer of the atmosphere. The blue light,having a shorter wavelength,is scattered away by the atmospheric particles,while the red light,having a longer wavelength,reaches our eyes.
At noon,the Sun is overhead,and the light travels a relatively shorter distance through the atmosphere. Consequently,only a small amount of blue and violet light is scattered,allowing the Sun to appear white as the majority of the light reaches our eyes.

(N/A) The person is suffering from Myopia (near-sightedness),as they cannot see distant objects clearly beyond a certain point ($12\, m$ in this case).
The corrective lens to be used is a Concave Lens (diverging lens).
$A$ concave lens diverges the incoming light rays from a distant object,making them appear to originate from the person's far point $(12\, m)$. This allows the eye lens to focus the image correctly on the retina.
The diagrams are as shown in the provided image.

(N/A) The defect of vision is Hypermetropia,also known as long-sightedness.
In this condition,the person can see distant objects clearly but cannot see nearby objects distinctly because the image of a nearby object is formed behind the retina.
It can be corrected by using a convex lens of suitable power,which converges the light rays before they enter the eye,allowing the image to be formed exactly on the retina.