Polarization by Reflection MCQ Quiz - Objective Question with Answer for Polarization by Reflection - Download Free PDF

The correct answer is 1.2 × 108 m/s.

Key Points

CONCEPT:

• Refractive index (μ): The ratio of the velocity of light in vacuum to the velocity of light in the medium is called refractive index of that medium.

\(\text{The refractive index of a substance/medium}=\frac{\text{Velocity of light in vacuum}}{\text{Velocity of light in the medium}}\)

So μ = c/v

Where c is the speed of light in vacuum and v is the speed of light in the medium.

CALCULATION:

Given that:

Refractive index of the diamond (µ_d)= 2.5

We know

The velocity of light in vacuum (c) = 3 × 10⁸ m/s

To find the velocity of light in diamond (v)

Now,

\(μ _d=\frac{c}{v}\\ or, \; 2.5= \frac{3 \times 10^8}{v}\\ or, \; v=\frac{3 \times 10^8}{2.5}=1.2\times 10^8 \; m/s\)     

Hence option 1 is correct.   

Calculation:
The number of waves in a medium is given by:

n = (thickness of medium) / (wavelength in that medium)

For the same number of waves to exist in both the water and the glass slab, the relationship between the number of waves in water and in glass can be expressed as:

Number of waves in water = Number of waves in glass

This can be written as:

(thickness of water) / (wavelength in water) = (thickness of glass) / (wavelength in glass)

Now, using the refractive index (n) to relate the wavelengths:

wavelength in medium = (wavelength in vacuum) / refractive index of medium

Let the refractive index of glass be "n_g" and the refractive index of water is given as 4/3. Substituting the values:

(5 cm) / (wavelength in water) = (4 cm) / (wavelength in glass)

Using the refractive index formula:

(5 cm) / (wavelength in vacuum / (4/3)) = (4 cm) / (wavelength in vacuum / n_g)

Solving for n_g:

n_g = (5/4) × (4/3) = 5/3

The correct answer is: 5/3

Concept:

Refractive Index: The refractive index (n) of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium.

• Formula: n = c / v
  • n = Refractive index
  • c = Speed of light in vacuum (3 × 10⁸ m/s)
  • v = Speed of light in the medium
• The refractive index of vacuum is exactly 1, as light travels at its maximum speed.
• For air, the refractive index is slightly greater than 1 due to the presence of molecules.

Calculation:

The refractive index of air with respect to vacuum is experimentally found to be:

⇒ n_air ≈ 1.00029

∴ The refractive index of air with respect to vacuum is 1.00029.

Calculation:

Apparent depth = Real depth / Refractive index

Apparent depth = 100 cm / (4/3) = 100 cm × (3/4) = 75 cm

The apparent depth of the object is 75 cm, which corresponds to option 4.

Calcultion:
The wavelength of light changes when it moves from one medium to another due to a change in its speed. The speed of light in any medium is given by:

v = c / n

The wavelength in any medium is related to its wavelength in vacuum by:

λ_medium = λ_vacuum / n

Given that the refractive index of air is approximately 1, and for the new medium n = 1.5, we can calculate the new wavelength in the medium:

λ_medium = 600 nm / 1.5 = 400 nm

The wavelength of light in the new medium is 400 nm. 

The correct answer is 1.2 × 108 m/s.

Key Points

CONCEPT:

• Refractive index (μ): The ratio of the velocity of light in vacuum to the velocity of light in the medium is called refractive index of that medium.

\(\text{The refractive index of a substance/medium}=\frac{\text{Velocity of light in vacuum}}{\text{Velocity of light in the medium}}\)

So μ = c/v

Where c is the speed of light in vacuum and v is the speed of light in the medium.

CALCULATION:

Given that:

Refractive index of the diamond (µ_d)= 2.5

We know

The velocity of light in vacuum (c) = 3 × 10⁸ m/s

To find the velocity of light in diamond (v)

Now,

\(μ _d=\frac{c}{v}\\ or, \; 2.5= \frac{3 \times 10^8}{v}\\ or, \; v=\frac{3 \times 10^8}{2.5}=1.2\times 10^8 \; m/s\)     

Hence option 1 is correct.   

Concept:

• Light is a form of energy which is an example of an electromagnetic wave.

• Wavelength: The distance between two successive crests or troughs is called wavelength of the wave.

• Refractive index: The ratio of the speed of light in air to the speed of light in the medium is called the refractive index of that medium.

\(Refractive\; index = \frac{{speed\;of\;light\;in\;air}}{{speed\;of\;light\;in\;medium}}\)

• White light consists of seven constituent colours: Violet (V), Indigo (I), Blue (B), Green (G), Yellow (Y), Orange (O), Red (R).

• The wavelength of the colour light in the order from lowest to highest is given as acronym VIBGYOR (V < I < B < G < Y < O < R):
• The wavelength range of visible light is 400 to 700 nm.

• The frequency of light remains the same on refraction because the frequency is independent of the medium.

Vair = λair f

Vmedium = λmedium f

\(\mu = \frac{{{\lambda _{air}}}}{{{\lambda _{medium}}}}\)

\(\mu \propto \frac{1}{\lambda }\)

• Since the refractive index of the medium is inversely proportional to the wavelength of the light.
• For violet light λ is minimum, hence the refractive index is maximum. 

Hence the correct option is Violet.

Concept:

• The absolute refractive index of a medium: The ratio of the speed of light in air or vacuum to the speed of light in the given medium is called the absolute refractive index of the medium.

\(μ = \frac{c}{v}\)

μ is the absolute refractive index, c is the speed of light in air, v is the speed of light in the given medium.

• Relative refractive index: The ratio of the speed of light in a transparent medium 1 to the speed of light in transparent medium 2 is called the refractive index of medium 2 with respect to medium 1.
• In general, the refractive index is a term used for an absolute refractive index. 
• Speed of light in air is approximately equal to 3 × 10 8 m /s 

Calculation:

Given Speed of light in vacuum c = 3 × 10 8 m /s 

speed of light in water v = ?

Refractive index of water μ = 1.33

So, 

\(μ = \frac{c}{v}\)

\(\implies 1.33 = \frac{3 \times 10^8}{v}\)

\(\implies v = \frac{3 \times 10^8}{1.33}\)

⇒ v = 2.25 × 108 m/s

So, the correct option is 2.25 × 108 m/s

Concept:

• Light is a form of energy which is an example of an electromagnetic wave.

• Wavelength: The distance between two successive crests or troughs is called wavelength of the wave.

• Refractive index: The ratio of the speed of light in air to the speed of light in the medium is called the refractive index of that medium.

\(Refractive\; index = \frac{{speed\;of\;light\;in\;vacuum}}{{speed\;of\;light\;in\;medium}}\)

• White light consists of seven constituent colours: Violet (V), Indigo (I), Blue (B), Green (G), Yellow (Y), Orange (O), Red (R).

• The wavelength of the colour light in the order from lowest to highest is given as acronym VIBGYOR (V < I < B < G < Y < O < R):
• The wavelength range of visible light is 400 to 700 nm.

Speed of light in air, v = 299,792,458 m/s

Speed of light in vacuum, c = 299,702,547 m/s

\(μ = \frac{{{c}}}{{{v}}}\)

μ = 1.003

μ ≈ 1​

CONCEPT:

• Refraction of Light: The bending of the ray of light passing from one medium to the other medium is called refraction.

• The refraction of light takes place on going from one medium to another because the speed of light is different in the two media.
• The greater the difference in the speeds of light in the two media, the greater will be the amount of refraction.
• A medium in which the speed of light is more is known as optically rarer medium and a medium in which the speed of light is less is known as an optically denser medium.

EXPLANATION:

Given - Real depth of the water tank = x, real depth of the water tank = 10 m and refractive index of water (μw) = 1.33

• The apparent depth is the distance of the virtual image from the surface of reference and the real depth is the distance of the real image from the surface of reference.

\(⇒ Refrective \; index=\frac{Real \;depth}{Apparent\;depth}\)

⇒ x = 1.33 × 10 = 13.3 m 

Brewster angle 'or' Polarising angle:

The angle of incidence at which a beam of unpolarized light falling on a transparent surface is reflected as a beam of completely plane polarised light is called polarising or Brewster angle.

This relation is known as Brewster law.

• When unpolarized light is incident on a reflecting surface, the reflected and refracted beams are partially polarized.
• The reflected beam is completely polarized when the angle of incidence equals the polarizing angle θp, which satisfies the equation \(\frac{{{n_2}}}{{{n_1}}} =\) then θp. 
• At this incident angle, the reflected and refracted rays are perpendicular to each other.

CONCEPT:

Refractive index: 

• The ratio of the speed of light in a vacuum to speed of light in a medium is called the refractive index of that medium.
• It is also called an absolute refractive index.

\({\rm{Refractive\;index\;}}\left( μ \right) = {\rm{\;}}\frac{{Speed\;of\;light\;in\;vaccum\left( C \right)}}{{Speed\;of\;light\;in\;a\;medium\left( v \right)}}\)

EXPLANATION:

Given - Refractive index (μ) = 1.5

• Mathematically the refractive index can be written as

\(⇒ {Speed\;of\;light\;in\;a\;medium\left( v \right)} = {\rm{\;}}\frac{{Speed\;of\;light\;in\;vaccum\left( C \right)}}{{\rm{Refractive\;index\;}}\left( μ \right)}\)

\(⇒ v = \frac{3 ×10^8}{1.5}=2× 10^8 \, m/s\)

Concept:

Refractive index: 

• The ratio of the speed of light in a vacuum to speed of light in a medium is called the refractive index of that medium.
• It is also called an absolute refractive index.
   

\({\rm{Refractive\;index}}\left( {\rm{\mu }} \right) = \frac{{{\rm{speed\;of\;light\;in\;vacuum\;}}\left( {\rm{c}} \right)}}{{{\rm{speed\;of\;light\;in\;medium\;}}\left( {\rm{v}} \right)}}\)

Calculation:

Given: μ_wa = 4/3, μ_ga = 3/2

\({{\rm{g}}_{{\rm{gw}}}} = \frac{{{{\rm{\mu }}_{{\rm{ga}}}}}}{{{{\rm{\mu }}_{{\rm{wa}}}}}} = \frac{{\frac{3}{2}}}{{\frac{4}{3}}} = \frac{9}{8}\)

\({{\bf{g}}_{{\bf{gw}}}}\; = \frac{9}{8}\)

CONCEPT:

• Refractive index (μ): The ratio of the speed of light in air to the speed of light in the medium is called the refractive index of that medium.

\(Refractive\; index = \frac{{speed\;of\;light\;in\;air(c)}}{{speed\;of\;light\;in\;medium (v)}} = c/v\)

CALCULATION:

Given that:

Refractive index of glass (μ) = 1.5

Speed of light in air (c) = 3 × 10⁸ m/s

Since μ = c/v

So the speed of light in glass (v) =\(\frac {c}{\mu}= \frac{(3 × 10^8 m/s)}{1.5} = 2 × 10^8 m/s\) 

Hence option 1 is correct.

Concept:

Angle of rotation:

If µ_R ,µ_L be the refractive indices of quartz crystal for right handed and left handed vibrations respectively (µ_L > µ_R ) then optical path difference on passing through a quartz crystal slab of thickness ‘t’ is given as,

Path difference = (µ_L - µ_R) t

If λ be the wavelength of light used, then phase difference will be 

\(\delta = \frac {2π}{λ} ({μ_L}-{μ_R}) t\)

Angle of rotation will be 

\(\frac{\delta}{2} = \frac {π}{λ} ({μ_L}-{μ_R}) t\)

Calculation:

Given μ_L =  1.5392; μ_R = 1.5391; t = 0.5 mm = 0.5 × 10^-3 m; λ = 762.9 nm = 762.9 × 10-9 m;

• The angle of rotation will be 

\(\frac{\delta}{2} = \frac {π}{762.9 × 10^{-9}} ({1.5392}-{1.5391}) 0.5\times 10^{-3} = 0.2058 \ radians\)

Converting radians to degrees,

Angle of rotation = 0.2058 × (180/π) = 11.79°