Refraction through a Prism and Dispersion Questions in English

(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 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.

(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 $D$.

(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.

(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.

(C) In the context of additive color mixing ($RGB$ model),the primary colors are Red,Green,and Blue. Secondary colors are formed by mixing two primary colors. Yellow is formed by mixing Red and Green. Cyan is formed by mixing Green and Blue. Maroon is a shade of red,not a standard secondary color in the additive model. However,in the context of basic physics questions regarding primary vs secondary colors,Green is a primary color,whereas Yellow,Cyan,and Magenta are secondary colors. Therefore,Green is the correct answer as it is a primary color.

(C) Complementary colors are pairs of colors that,when combined or mixed,cancel each other out to produce a grayscale color like white or black.
In the context of additive color theory (light),the primary colors are Red,Green,and Blue.
The complementary color of Red is Cyan (a mixture of Green and Blue).
Therefore,Red and Cyan are considered complementary colors.

(B) In the context of additive color theory ($RGB$ model),the complementary color of red is cyan.
Cyan is formed by the combination of green and blue light.
When red light is mixed with cyan light,it produces white light,which is the definition of complementary colors.

(C) In the context of additive color theory ($RGB$ model),the complementary color is the color that,when added to a primary color,produces white light.
For green light,the complementary color is magenta.
Magenta is formed by the combination of red and blue light.
Therefore,green and magenta are complementary colors.

(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. The sunlight undergoes refraction,dispersion,and internal reflection within the droplets. According to the spectrum of white light $(VIBGYOR)$,the color with the longest wavelength,which is $Red$,deviates the least and appears at the outermost (top) edge of the rainbow,while the color with the shortest wavelength,$Violet$,deviates the most and appears at the innermost (bottom) edge.

(B) rainbow is an optical phenomenon caused by the reflection,refraction,and dispersion of light in water droplets.
For a rainbow to be visible,the sun must be behind the observer and the water droplets must be in front.
In the morning,the sun rises in the East. Therefore,for the sun to be behind the observer,the observer must be facing West.
Thus,a rainbow formed in the morning is always seen in the West.

(D) The brilliance of a diamond is primarily due to the phenomenon of $Total \text{ } Internal \text{ } Reflection$ $(TIR)$.
When light enters a diamond, it undergoes multiple internal reflections because the critical angle for a diamond-air interface is very small (approximately $24^{\circ}$).
Due to its high refractive index and precise cutting, light rays entering the diamond are repeatedly reflected internally until they emerge from the top facets, giving the diamond its characteristic sparkle and brilliance.

(D) The formation of a rainbow is a complex optical phenomenon that involves multiple processes occurring within water droplets in the atmosphere.
$1$. Sunlight enters a water droplet and undergoes refraction and dispersion,splitting the white light into its constituent colors.
$2$. The light then undergoes internal reflection at the back surface of the droplet.
$3$. Finally,the light undergoes refraction again as it exits the droplet.
Therefore,refraction,dispersion,and internal reflection are all involved in the formation of a rainbow.