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

(A) When light rays enter the human eye,they first encounter the cornea.
The cornea is the transparent,curved,outermost layer of the eye.
Because the cornea has a significant difference in refractive index compared to the air outside,it is responsible for the majority of the refraction of light entering the eye.
The crystalline lens provides the fine-tuning of the focus,but the primary bending of light occurs at the outer surface of the cornea.

(D) At sunrise or sunset,the sun is near the horizon.
Light from the sun has to travel a larger distance through the atmosphere of the Earth to reach our eyes.
During this journey,most of the blue and shorter wavelengths of light are scattered away by the atmospheric particles.
Only the light of longer wavelengths,such as red,is able to reach our eyes.
Therefore,the sun appears reddish at sunrise or sunset due to the scattering of light.

(A) In a vacuum or air,all colours of white light travel with the same speed,which is approximately $3 \times 10^8 \ m/s$.
While light of different colours travels at different speeds in a medium like glass or water (leading to dispersion),they do not exhibit this difference in air.
Therefore,all colours of white light propagate at the same speed in air.

(B) The formation of a rainbow is a natural spectrum appearing in the sky after a rain shower.
It is caused by the dispersion of sunlight by tiny water droplets,present in the atmosphere.
These water droplets act like small prisms.
They refract and disperse the incident sunlight,then reflect it internally,and finally refract it again when it comes out of the raindrop.
Therefore,the phenomena involved are refraction,dispersion,and total internal reflection.

(D) The focal length of the eye lens is controlled by the ciliary muscles.
When the ciliary muscles are relaxed,the suspensory ligaments become taut,which pulls the lens and makes it thinner.
$A$ thinner lens has a greater radius of curvature,which results in an increased focal length,allowing the eye to focus on distant objects.
Therefore,the focal length increases when the eye muscles are relaxed and the lens becomes thinner.

(D) At noon,the sun is overhead,and the light from the sun has to travel a relatively shorter distance through the Earth's atmosphere to reach the observer.
Because the distance is short,only a small amount of blue and violet light is scattered.
Since most of the light reaches the observer without significant scattering,the sun appears white to us.

(A) When white light passes through a prism,it disperses into its constituent colours: Violet,Indigo,Blue,Green,Yellow,Orange,and Red $(VIBGYOR)$.
In a standard prism orientation (where the base is at the bottom),the colours appear in the order $VIBGYOR$ from bottom to top.
If the prism is inverted (base at the top),the order of colours from top to bottom is $VIBGYOR$.
The third colour from the top in the inverted prism is Blue,which corresponds to the colour of the sky.
In the given options,case $(i)$ shows the prism with the vertex $A$ at the bottom,which is an inverted orientation. Therefore,the third colour from the top will be Blue.

(C) The person is suffering from myopia (near-sightedness) because they cannot see objects beyond $2\, m$.
To correct this defect, a concave lens is used to bring the image of an object at infinity to the person's far point $(2\, m)$.
Here, the object distance $u = \infty$ and the image distance $v = -2\, m$.
Using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$.
Substituting the values: $\frac{1}{f} = \frac{1}{-2} - \frac{1}{\infty} = -0.5\, m^{-1}$.
Since power $P = \frac{1}{f(\text{in meters})}$, we get $P = -0.5\, D$.

(B) The statement is False.
Accommodation is the ability of the eye to focus on objects at varying distances by changing the focal length of the eye lens with the help of ciliary muscles.
The adjustment of the amount of light entering the eye is controlled by the iris and the pupil,not by accommodation.

(B) The statement is $False$.
Myopia,or near-sightedness,is a defect of vision in which a person can see nearby objects clearly but cannot see distant objects distinctly.
While the statement says they can see 'only' nearer objects,it is important to clarify that the primary characteristic of myopia is the inability to see distant objects clearly,rather than a limitation that prevents them from seeing anything else.
However,in the context of standard physics problems,this statement is often considered false because it implies an exclusive capability that ignores the definition of the defect as a failure to focus on distant objects.

(B) Presbyopia is a defect of vision in which an old person cannot see the nearby objects clearly due to the loss of accommodation power of the eye. It is not a type of far-sightedness (hypermetropia),although it shares some similarities in terms of corrective lenses. Therefore,the statement is False.

(A) Long-sightedness,also known as $Hypermetropia$,is a defect of vision where a person can see distant objects clearly but cannot see nearby objects distinctly. This happens because the light rays from a nearby object focus behind the retina. $A$ convex lens is used to converge the light rays before they enter the eye,allowing the image to be focused correctly on the retina. Therefore,the statement is $True$.

(A) Astigmatism is a common vision condition caused by an irregularly shaped cornea or lens,which prevents light from focusing properly on the retina. This results in blurred or distorted vision at all distances. To correct this refractive error,a cylindrical lens is used,which compensates for the uneven curvature of the eye by providing different refractive powers in different meridians. Therefore,the statement is true.

(A) Short-sightedness,also known as myopia,is a defect of vision in which a person can see nearby objects clearly but cannot see distant objects distinctly.
This condition occurs because the eyeball becomes too long,causing the light rays from distant objects to focus in front of the retina instead of directly on it.
Therefore,the statement is True.

(A) The statement is $True$.
Defects of vision occur when the eye loses its ability to accommodate or focus light properly on the retina.
Common examples include myopia (nearsightedness),hypermetropia (farsightedness),and presbyopia.

(A) Myopia,also known as near-sightedness,is a common vision condition in which near objects appear clear,but objects far away look blurry.
In a myopic eye,the light rays from a distant object converge at a point in front of the retina instead of directly on the retina.
This occurs because the eyeball becomes too long or the cornea is too curved,causing the image to focus before reaching the retina.
Therefore,the statement is True.

(A) The light emitted by the sun is known as white light. When this light passes through a prism or is dispersed by water droplets in the atmosphere (as in a rainbow),it splits into its constituent seven colours: Violet,Indigo,Blue,Green,Yellow,Orange,and Red $(VIBGYOR)$. Therefore,the statement is true.

(A) When white light passes through a prism,it splits into its constituent colours (dispersion).
According to Cauchy's equation,the refractive index of a material depends on the wavelength of light.
The refractive index is higher for shorter wavelengths (violet) and lower for longer wavelengths (red).
Since the angle of deviation is directly related to the refractive index,violet light (having the shortest wavelength) undergoes the maximum deviation (bends the most),while red light (having the longest wavelength) undergoes the minimum deviation (bends the least).

(B) The statement is $False$. In a transparent medium (other than a vacuum),the speed of light depends on its wavelength (or frequency). This phenomenon is known as dispersion. Different colours of light have different wavelengths; therefore,they travel at different speeds in a medium like glass or water. Violet light,having a shorter wavelength,travels slower than red light,which has a longer wavelength.

(A) The phenomenon of dispersion is the splitting of white light into its constituent colours when it passes through a transparent medium like a glass prism.
This occurs because the refractive index of the medium is different for different wavelengths (colours) of light.
Since the speed of light in a medium is given by $v = c/n$ (where $c$ is the speed of light in vacuum and $n$ is the refractive index),different colours travel at different speeds in the medium.
Consequently,each colour undergoes a different amount of deviation,leading to the separation of colours.

(C) The phenomenon of splitting of white light into its seven constituent colors (violet, indigo, blue, green, yellow, orange, and red) when passing through a glass prism is known as $Dispersion$ of light. This occurs because different colors of light travel at different speeds in the glass medium, causing them to bend by different angles.

(A) When white light passes through a prism,it splits into its constituent colors due to the difference in the refractive index of the glass for different wavelengths.
According to Cauchy's equation,the refractive index is inversely proportional to the wavelength of light.
Violet light has the shortest wavelength among the visible spectrum,which results in the highest refractive index for violet light in the glass prism.
Consequently,violet light undergoes the maximum deviation,while red light,having the longest wavelength,undergoes the minimum deviation.

(D) In the context of light and color vision,the primary colors are Red,Green,and Blue $(RGB)$.
These colors are considered primary because they cannot be created by mixing other colors,and they can be combined in various intensities to produce a wide spectrum of other colors.
Therefore,the correct option is $D$.

(C) The primary colours of light are $Red$,$Green$,and $Blue$ $(RGB)$.
These colours are considered primary because they cannot be created by mixing other colours of light,but when combined in various intensities,they can produce a wide range of colours,including white light.

(C) In the human eye,light enters through the cornea and passes through the pupil. The eye lens focuses this light to form a real and inverted image on the light-sensitive screen located at the back of the eye,which is called the retina. Therefore,the correct option is $C$.

(D) In the context of additive color theory ($RGB$ model),the complementary color of blue is yellow.
When blue light is combined with yellow light,they produce white light.
Therefore,yellow is the complementary color to blue.

(C) When mixing primary colors of light,red and blue combine to produce magenta. This is a standard result in the additive color model used in physics and optics.

(C) The focal length of the eye lens is adjusted by the $Ciliary muscles$.
When the $Ciliary muscles$ contract, the curvature of the lens increases, making it thicker, which decreases the focal length.
When the $Ciliary muscles$ relax, the lens becomes thinner, which increases the focal length.
This process is known as the accommodation of the eye.

(B) pigment appears blue because it absorbs all other colors of the visible spectrum except blue.
When white light (which consists of $VIBGYOR$) falls on a blue pigment,the pigment absorbs colors like red,orange,yellow,and green.
It reflects the blue light back to our eyes.
However,in the context of pigments and color mixing,a blue pigment often reflects a range of wavelengths in the blue-green region.
Among the given options,the combination that best describes the reflected light from a blue pigment is violet,green,and blue,as these are closer to the blue end of the spectrum.

(C) $Presbyopia$ is a vision defect that occurs due to the gradual weakening of ciliary muscles and diminishing flexibility of the eye lens with aging. This condition makes it difficult for a person to see nearby objects clearly. To correct this defect,a $Bifocal$ lens is used,which consists of both concave and convex lenses. The upper part of the lens is concave (for distant vision) and the lower part is convex (for near vision).

(D) The formation of a rainbow is a combined effect of three optical phenomena:
$1$. Refraction: Light enters the water droplet and bends.
$2$. Dispersion: White light splits into its constituent colors $(VIBGYOR)$ inside the droplet.
$3$. Internal Reflection: Light reflects off the inner surface of the droplet.
Absorption is not a process involved in the formation of a rainbow. Therefore,the correct option is $D$.

(C) Total internal reflection $(TIR)$ occurs when light travels from a denser medium to a rarer medium.
For $TIR$ to take place,two conditions must be satisfied:
$1$. Light must travel from an optically denser medium to an optically rarer medium.
$2$. The angle of incidence $(i)$ must be greater than the critical angle $(c)$ for the pair of media $(i > c)$.

(C) Myopia,also known as nearsightedness,is a defect of vision in which a person can see nearby objects clearly but cannot see distant objects distinctly.
In a myopic eye,the image of a distant object is formed in front of the retina because the eyeball becomes too long or the curvature of the lens is too high.
Therefore,the correct option is $C$.

(B) The twinkling of stars is due to atmospheric refraction of starlight.
As starlight enters the Earth's atmosphere,it undergoes continuous refraction due to the changing refractive index of different layers of air.
These layers have varying temperatures and densities,causing the light to bend as it passes through them.
This continuous bending of light causes the apparent position of the star to fluctuate slightly,and the amount of light reaching the eye varies,resulting in the twinkling effect.

(C) The Tyndall effect is the phenomenon in which the particles in a colloid or a fine suspension scatter the beams of light that are directed at them.
This scattering of light by colloidal particles is known as the Tyndall effect.
Therefore,the correct phenomenon responsible for the Tyndall effect is scattering.

(C) Due to atmospheric refraction,the Sun is visible to us about $2$ minutes before the actual sunrise and about $2$ minutes after the actual sunset.
As the light from the Sun enters the Earth's atmosphere,it bends due to the varying refractive indices of the air layers.
This bending causes the Sun to appear slightly higher than its actual position,leading to an apparent delay in sunset by approximately $2$ minutes.

(A) According to Rayleigh 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 red, yellow, and green light, it undergoes the maximum scattering by the particles present in the atmosphere.
Therefore, the correct option is $A$.

(D) When white light passes through a prism,it undergoes dispersion into its constituent colors.
Different colors travel at different speeds within the medium of the prism.
The refractive index $(n)$ of a material is related to the velocity of light $(v)$ by the formula $n = c/v$,where $c$ is the speed of light in a vacuum.
According to Cauchy's dispersion formula,the refractive index is higher for light with a shorter wavelength.
Violet light has the shortest wavelength in the visible spectrum,which results in the highest refractive index for the prism material for violet light.
Since $v = c/n$,a higher refractive index $(n)$ leads to a lower velocity $(v)$.
Therefore,violet light travels with the minimum velocity in a prism.

(B) When white light passes through a prism,it splits into its constituent colors due to the difference in their refractive indices in the glass medium.
According to the relation $v = c/n$,where $v$ is the velocity of light in the medium,$c$ is the speed of light in a vacuum,and $n$ is the refractive index of the medium.
The refractive index $n$ is inversely proportional to the wavelength $\lambda$ of the light.
Red light has the longest wavelength,which results in the lowest refractive index for the glass prism.
Since the refractive index is lowest for red light,its velocity $v$ is the maximum among all the colors of the visible spectrum.

(D) When white light passes through a prism,it splits into its constituent colors due to the difference in the refractive index of the glass for different wavelengths.
According to Cauchy's equation,the refractive index is inversely proportional to the wavelength of light.
Red light has the longest wavelength in the visible spectrum,which results in the lowest refractive index for red light in the prism.
Since the angle of deviation is directly related to the refractive index,the light with the lowest refractive index undergoes the minimum deviation.
Therefore,red light deviates the least,while violet light,having the shortest wavelength,deviates the most.

(C) When white light passes through a prism,it splits into its constituent seven colors,known as the spectrum,represented by the acronym $VIBGYOR$.
The order of colors from the bottom (least deviated) to the top (most deviated) is: $Violet, Indigo, Blue, Green, Yellow, Orange, Red$.
Counting from either end,the color located exactly in the middle of the $VIBGYOR$ sequence is $Green$ $(G)$.

(A) Sir Isaac Newton was the first to demonstrate through his prism experiments that white light is composed of a spectrum of seven colors (Violet,Indigo,Blue,Green,Yellow,Orange,and Red). He used a glass prism to split white light into its constituent colors and then used a second inverted prism to recombine them back into white light.

(D) An object appears to be a certain color because it reflects that specific color of light and absorbs all other colors.
$A$ red rose appears red because it reflects red light and absorbs all other colors of the visible spectrum.
When green light is incident on a red rose,the rose absorbs the green light and reflects almost nothing.
Since no light is reflected back to our eyes,the rose appears black.

(A) White light is composed of seven colors $(VIBGYOR)$. When an object reflects all the constituent colors of white light,it does not absorb any of them. Since all colors are reflected back to our eyes,the object appears white. If an object absorbs all colors,it appears black.

(D) The color of an object is determined by the light it reflects to our eyes.
When white light (which consists of $7$ colors) falls on an object,the object absorbs some colors and reflects others.
The reflected light reaches our eyes,and our brain perceives the object as having that specific color.
If an object absorbs all the component colors of white light and reflects none of them,no light reaches our eyes from the object.
Therefore,the object appears black.

(A) The process of creating a wide range of colors by combining primary colors (such as Red, Green, and Blue) in different proportions is known as $Additive$ $\text{color mixing}$.
In this method, light of different wavelengths is added together to produce new colors.
For example, mixing Red and Green light produces Yellow light.
Therefore, the correct option is $A$.

(C) The colors obtained by mixing primary colors (such as Red,Green,and Blue in the context of light) are known as secondary colors.
When primary colors are combined in different proportions,they produce a wide range of secondary colors.
For example,mixing Red and Green light produces Yellow,Green and Blue produces Cyan,and Red and Blue produces Magenta.

(D) In the context of additive color mixing (light),the primary colors are $Red$,$Green$,and $Blue$ $(RGB)$.
These colors are considered primary because they cannot be created by mixing other colors,and they can be combined in various intensities to produce a wide range of other colors.
$Yellow$ is a secondary color formed by mixing $Red$ and $Green$ light.
Therefore,$Yellow$ is not a primary color.

(B) The color maroon is a dark shade of red. In the context of additive color mixing (light),maroon is produced by combining red light with a smaller proportion of blue light. Therefore,the combination of red and blue light results in the formation of maroon.

(B) The mixing of light colors follows the additive color mixing principle.
When blue light and green light are superimposed or overlap,they produce cyan light.
This is a fundamental concept in the $RGB$ (Red,Green,Blue) color model where cyan is the secondary color formed by the combination of green and blue.