Refraction through a Prism and Dispersion Questions in English

(A) prism is a transparent optical element with flat,polished surfaces that refract light.
It is typically a glass object with two triangular bases and three rectangular lateral surfaces inclined at an angle to each other.

(C) When white light passes through a prism,it disperses into its constituent colours: Violet,Indigo,Blue,Green,Yellow,Orange,and Red $(VIBGYOR)$.
The light bends towards the base of the prism.
In case $(i)$,the base is $BC$. The light enters through face $AB$ and bends towards the base $BC$. The order of colours from top to bottom will be $Red, Orange, Yellow, Green, Blue, Indigo, Violet$.
The third colour from the top is Yellow.
In case $(ii)$,the prism is inverted,so the base is $BC$ at the top. The light bends towards the base (upwards). The order of colours from top to bottom will be $Violet, Indigo, Blue, Green, Yellow, Orange, Red$.
The third colour from the top is Blue,which corresponds to the colour of the sky.
Therefore,case $(ii)$ is the correct orientation.

(B) The formation of a rainbow is a natural phenomenon caused by the dispersion of sunlight by tiny water droplets present in the atmosphere.
$1$. Refraction: As sunlight enters the water droplet,it bends due to the change in medium.
$2$. Dispersion: The white light splits into its constituent colors $(VIBGYOR)$ inside the droplet.
$3$. Total Internal Reflection: The light rays strike the inner surface of the droplet and are reflected back.
$4$. Refraction: Finally,the light rays refract again as they exit the droplet,reaching the observer's eye.
Therefore,the correct combination of phenomena is refraction,dispersion,and total internal reflection.

(D) In a vacuum or air,all colours of white light travel with the same speed,which is approximately $3 \times 10^8 \ m/s$. Dispersion and differences in speed for different colours only occur when light travels through a dispersive medium like glass or water. Therefore,in air,all colours of white light move with the same speed.

(N/A) To obtain a beam of white light from a narrow beam of white light after passing through two prisms,the two identical prisms must be placed in an inverted position with respect to each other.
When a beam of white light enters the first prism $(P_1)$,it undergoes dispersion and splits into its constituent seven colors.
When these dispersed rays fall on the second prism $(P_2)$,which is placed in an inverted position,it recombines the colors to form a beam of white light that emerges from the second prism.

(N/A) When a narrow beam of white light is incident on one of the refracting surfaces of a glass prism,it splits into its constituent seven colours. This phenomenon is known as the dispersion of light.
The order of colours in the spectrum obtained,from the base of the prism upwards,is Violet $(V)$,Indigo $(I)$,Blue $(B)$,Green $(G)$,Yellow $(Y)$,Orange $(O)$,and Red $(R)$. This is commonly remembered by the acronym $VIBGYOR$.
Red light bends the least,while violet light bends the most because the refractive index of glass is different for different wavelengths of light.

(B) 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.
Due to the dispersion of light and internal reflection,we see a spectrum of colours in the form of a rainbow.

(N/A) $1$. Refraction through a prism: When a light ray $PQ$ enters a triangular glass prism $ABC$,it undergoes refraction at the first surface $AB$ and bends towards the normal $NN'$.
$2$. Inside the prism,the ray travels as $EF$ and bends away from the normal $MM'$ at the second surface $AC$,emerging as ray $FS$.
$3$. The incident ray $PQ$ is extended forward,and the emergent ray $FS$ is extended backward to meet at point $G$.
$4$. Angle of deviation: The angle $D$ formed between the direction of the incident ray and the direction of the emergent ray is known as the angle of deviation.

(N/A) Dispersion is the phenomenon of splitting of white light into its constituent colours when it passes through a glass prism.
When a beam of white light enters a glass prism,it gets refracted and splits into a band of seven colours: Violet,Indigo,Blue,Green,Yellow,Orange,and Red $(VIBGYOR)$.
This splitting occurs because different colours of light travel at different speeds in the glass medium,and thus,they undergo different amounts of deviation.
Violet light bends the most because it has the shortest wavelength,while red light bends the least because it has the longest wavelength.
The resulting band of colours is called a spectrum.

(C) The visible spectrum consists of seven colours,commonly remembered by the acronym $VIBGYOR$.
These colours are Violet,Indigo,Blue,Green,Yellow,Orange,and Red.

(N/A) The phenomenon of splitting of white light into its constituent colours (spectrum) when it passes through a transparent medium like a glass prism is known as dispersion of light.

(N/A) The rainbow formed in the sky after a rainy day is a natural phenomenon that demonstrates the dispersion of white light. When sunlight passes through tiny water droplets suspended in the atmosphere,these droplets act like small prisms,refracting and dispersing the white light into its constituent seven colors.

(A) The phenomenon of the dispersion of light,which is the splitting of white light into its constituent colors (the spectrum) when passing through a prism,was first explained by Sir Isaac Newton in the $17^{th}$ century.

(A) When a beam of white light passes through a glass prism,it undergoes dispersion into its constituent seven colours.
$(i)$ The colour that suffers the least deviation is Red because it has the longest wavelength and travels fastest in the glass medium.
$(ii)$ The colour that suffers the maximum deviation is Violet because it has the shortest wavelength and travels slowest in the glass medium.

(N/A) The formation of a rainbow is primarily caused by the following two phenomena:
$(i)$ Dispersion: When sunlight enters a water droplet,it splits into its constituent colors due to the difference in refractive indices for different wavelengths.
$(ii)$ Total Internal Reflection: After dispersion,the light rays strike the inner surface of the water droplet and are reflected back inside,which is known as total internal reflection.

(N/A) When white light passes through a prism,it splits into its constituent colours due to the difference in their wavelengths and refractive indices. The red light has the longest wavelength and travels the fastest in the glass medium,resulting in the least deviation. Conversely,the violet light has the shortest wavelength and travels the slowest,resulting in the most deviation. Therefore,the component that deviates the least is red,and the component that deviates the most is violet.

(A) The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye.
Visible light typically has a wavelength range from approximately $380 \; nm$ to $750 \; nm$.
Converting these values to meters: $380 \; nm = 380 \times 10^{-9} \; m = 3.8 \times 10^{-7} \; m$ and $750 \; nm = 750 \times 10^{-9} \; m = 7.5 \times 10^{-7} \; m$.
Rounding these values,the range is approximately $4 \times 10^{-7} \; m$ to $8 \times 10^{-7} \; m$.

(A) The visible spectrum of light ranges from approximately $0.4 \,\mu m$ to $0.7 \,\mu m$.
Violet light has the shortest wavelength, which is approximately $0.4 \,\mu m$.
Red light has the longest wavelength, which is approximately $0.7 \,\mu m$.
Therefore, the longest wavelength (red) is $0.7 \,\mu m$ and the shortest wavelength (violet) is $0.4 \,\mu m$.

(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) 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.

(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) 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) 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.

(B) $(i)$ The phenomenon of splitting of white light into its constituent colours (spectrum) when passing through a glass prism is called dispersion of light.
$(ii)$ The deviation of light depends on its refractive index in the medium. $A$ higher deviation implies a higher refractive index,and since refractive index is inversely proportional to the speed of light in that medium $(n = c/v)$,the colour that deviates more $(A)$ travels slower. Therefore,the colour that deviates less $(B)$ has a higher speed in the prism.

(N/A) rainbow is a natural spectrum appearing in the sky after a rainfall. It is caused by the dispersion of sunlight by tiny water droplets present in the atmosphere.
$1$. When sunlight enters a water droplet,it undergoes refraction and dispersion.
$2$. The light then undergoes internal reflection inside the droplet.
$3$. Finally,the light undergoes refraction again as it exits the droplet.
Due to these phenomena (refraction,dispersion,and internal reflection),different colours reach the observer's eye at different angles,resulting in the formation of a rainbow. The observer must always have their back towards the Sun to see a rainbow.

(N/A) The cause of dispersion is that white light is composed of different colours,each having a different wavelength.
When white light enters a glass prism,each colour travels at a different speed within the medium.
Because the refractive index of glass is different for different wavelengths,each colour bends through a different angle with respect to the incident ray.
Specifically,red light has the longest wavelength and bends the least,while violet light has the shortest wavelength and bends the most.
As a result,the rays of each colour emerge along different paths,becoming distinct and forming a band of colours known as a spectrum.
The diagram is as shown below:

(N/A) prism $P_{1}$ in the path of white light disperses it into various colours. The red rays are deviated the least and the violet rays are deviated the most. The second prism $P_{2}$ is placed in an inverted position relative to $P_{1}$ such that its refracting edge is at the bottom. The second refracting surface of $P_{1}$ and the first refracting surface of $P_{2}$ are parallel. The dispersion produced by $P_{1}$ is neutralised by $P_{2}$. The colours recombine in prism $P_{2}$ and a beam of white light emerges from it.
$(b)$ Isaac Newton.
$(c)$ Spectrum: It is the band of coloured components of light $(VIBGYOR)$ that is obtained when a beam of white light is passed through a glass prism.

(N/A) The labelled diagram is as shown in the provided image.
Here,the components are as follows:
$(a)$ $PE$ - Incident ray
$(b)$ $FS$ - Emergent ray
$(c)$ $EF$ - Refracted ray
$(d)$ $\angle i$ - Angle of incidence
$(e)$ $\angle D$ - Angle of deviation
$(f)$ $\angle e$ - Angle of emergence

(N/A) Dispersion: The splitting of white light into its constituent seven colours is called dispersion of light.
Cause: Ordinary white light is a superposition of waves of wavelengths extending throughout the visible spectrum. The speed of light in a vacuum is the same for all wavelengths,but the speed in a material substance is different for different wavelengths. As a result,different colours are deviated by different angles when they pass through a prism. This is called dispersion of light.
$(b)$ In a prism,the refraction of light takes place at the two slant surfaces. The dispersion of white light occurs at the first surface of the prism where its constituent colours are deviated through different angles. At the second surface,these split colours undergo further refraction and get separated more. However,in a rectangular glass slab,the refraction of light takes place at two parallel surfaces. At the first surface,although the white light splits into its constituent colours on refraction,these split colours,upon undergoing refraction at the second parallel surface,emerge as a parallel beam,which gives the impression of white light.

(N/A) As a result of dispersion produced by the prism,the white light is split up into seven colours. These colours are represented by the acronym '$VIBGYOR$' in the order of increasing deviation: $1$ (Red),$2$ (Orange),$3$ (Yellow),$4$ (Green),$5$ (Blue),$6$ (Indigo),$7$ (Violet). Thus,the colour at position $3$ is yellow and at position $5$ is blue. The student's statement is incorrect because the sky is blue and gold is yellow,which corresponds to positions $5$ and $3$ respectively,not $3$ and $5$.
$(b)$ The positions of the colours of the given objects are represented by:
$(i)$ Brinjal (Violet) $- 7$
$(ii)$ Danger signal (Red) $- 1$
$(iii)$ Neel (Indigo) $- 6$
$(iv)$ Orange (Orange) $- 2$

(N/A) Take a thick sheet of cardboard and make a small hole or narrow slit in its middle. Allow sunlight to fall on the narrow slit. This gives a narrow beam of white light. Now,take a glass prism and allow the light from the slit to fall on one of its faces as shown in the figure.
Turn the prism slowly until the light that comes out of it appears on a nearby screen. We will observe that sunlight has split into seven colours. This shows that sunlight is made up of seven colours.
$(b)$ Red colour bends least while violet colour bends the most. The different colours bend at different angles with respect to the incident ray due to refraction. This happens because the speed of light of different colours is different in the glass medium,leading to different refractive indices for different wavelengths.

(N/A) The diagram is as shown in the reference image.
$(i)$ The phenomenon is called the dispersion of light. It occurs because different wavelengths of light travel with different speeds in the glass prism,causing them to bend at different angles.
$(ii)$ This phenomenon is observed in nature in the formation of a rainbow.
$(iii)$ White light consists of seven different colors (wavelengths),which are violet,indigo,blue,green,yellow,orange,and red.

(N/A) In a prism,the refraction of light takes place at two slant surfaces that are not parallel to each other. The dispersion of white light occurs at the first surface of the prism,where its constituent colours are deviated through different angles. At the second surface,these split colours undergo further refraction and separation,resulting in a spectrum.
In a rectangular glass block,the refraction of light takes place at two parallel surfaces. At the first surface,white light splits into its constituent colours upon refraction. However,because the second surface is parallel to the first,these split colours undergo refraction at the second surface in such a way that they emerge as a parallel beam,which recombines to give the impression of white light.

(N/A) The colours at positions $3$ and $5$ are yellow and blue respectively. The student has identified them as yellow (i.e.,colour of the core of a hard-boiled egg) and blue (i.e.,colour of the sky) respectively. Hence,the statement is correct.
$(b)$ $(i)$ Position $7$ is the position of violet colour,which corresponds to the colour of a solution of potassium permanganate.
$(ii)$ Position $1$ is the position of red colour,which corresponds to the colour of danger or stop signal lights.

(N/A) To represent the refraction of a light ray through a prism,we follow these steps:
$1$. Draw a triangular prism $ABC$.
$2$. Draw an incident ray $PQ$ striking the face $AB$.
$3$. Draw a normal $N$ at the point of incidence $Q$ on face $AB$.
$4$. The angle between the incident ray $PQ$ and the normal $N$ is the angle of incidence,denoted by $i$.
$5$. The refracted ray $QR$ travels inside the prism. The angle between the refracted ray $QR$ and the normal $N$ at face $AB$ is the angle of refraction,denoted by $r_1$.
$6$. At face $AC$,the ray emerges as $RS$. Draw a normal $N'$ at the point of emergence $R$.
$7$. The angle between the emergent ray $RS$ and the normal $N'$ is the angle of emergence,denoted by $e$.
$8$. Extend the incident ray $PQ$ forward and the emergent ray $RS$ backward to meet at a point $D$. The angle between these two lines is the angle of deviation,denoted by $\delta$.

(N/A) In the minimum deviation position, the refracted ray inside the prism is parallel to the base $BC$. The emergent ray is shown in the provided solution image.
The angle of deviation $\delta$ depends upon the following factors:
$(i)$ The angle of the prism $(A)$.
$(ii)$ The refractive index of the material of the prism $\mu$.
$(iii)$ The angle of incidence $(i)$.
$(iv)$ The wavelength of the light used $\lambda$.

(N/A) We have the angle of incidence at the face $AB = 0^{\circ}$ as the ray $PQ$ falls normally on this face.
The normally incident ray $PQ$ passes through the prism undeviated and strikes the face $AC$ at the point $R$.
We draw the normal $MN$ to the face $AC$ at the point $R$.
The angle of incidence at the point $R$ is the angle $NRQ$.
From the geometry of the equilateral triangle $ABC$,the angle at vertex $A$ is $60^{\circ}$. In the triangle formed by the ray $PQ$ and the sides of the prism,the angle at $Q$ is $90^{\circ}$ and the angle at $A$ is $60^{\circ}$,so the angle at $R$ inside the triangle is $180^{\circ} - (90^{\circ} + 60^{\circ}) = 30^{\circ}$.
Since $MN$ is normal to $AC$,the angle of incidence $i = 90^{\circ} - 30^{\circ} = 60^{\circ}$.
Hence,the angle of incidence at face $AB = 0^{\circ}$ and the angle of incidence at face $AC = 60^{\circ}$.

$(i)$ No, the images of letters of different colours will be raised by slightly different heights.
$(ii)$ The letter $V$, corresponding to the violet colour, will be raised to the maximum. This is because the apparent depth is given by the formula: $\text{Apparent depth} = \frac{\text{Real depth}}{n}$. Since the refractive index $n$ is maximum for the violet colour, its apparent depth will be the least. Consequently, the shift (raised height) is maximum for the violet colour.

(A) When white light passes through a prism,it splits into its component colours,a phenomenon known as dispersion.
According to Cauchy's dispersion formula,the refractive index of a material depends on the wavelength of the light.
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 the prism material.
Since the angle of deviation is directly related to the refractive index,the colour with the lowest refractive index undergoes the least deviation.
Therefore,red light is deviated the least,while violet light,having the shortest wavelength,is deviated the most.

(B) The visible spectrum of light follows the order of $VIBGYOR$ (Violet, Indigo, Blue, Green, Yellow, Orange, Red).
In this spectrum, the wavelength $\lambda$ increases from violet to red.
Comparing the given colors: Blue, Green, and Yellow.
According to the $VIBGYOR$ sequence, the order of increasing wavelength is: $\lambda_{\text{blue}} < \lambda_{\text{green}} < \lambda_{\text{yellow}}$.
Therefore, the correct order of decreasing wavelength is $\lambda_{\text{yellow}} > \lambda_{\text{green}} > \lambda_{\text{blue}}$.

(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.

(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.

(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.

(B) The wavelength range of visible light is approximately $400 \; nm$ to $750 \; nm$ (often rounded to $400 \; nm$ to $800 \; nm$).
To convert nanometers $(nm)$ to centimeters $(cm)$:
$1 \; nm = 10^{-9} \; m = 10^{-7} \; cm$.
Therefore,$400 \; nm = 400 \times 10^{-7} \; cm = 4 \times 10^{-5} \; cm$.
Similarly,$800 \; nm = 800 \times 10^{-7} \; cm = 8 \times 10^{-5} \; cm$.
Thus,the range is $4 \times 10^{-5} \; cm$ to $8 \times 10^{-5} \; cm$.