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Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

The index of refraction for diamond is $2.42$. For a diamond in the air (index of refraction = $1.00$), what is the smallest angle that a light ray inside the diamond can make with a normal and completely reflect back inside the diamond (the critical angle)?

  1. $90^o$
  2. $45^o$
  3. $68^o$
  4. $66^o$
  5. $24^o$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation
Given :   $n _{a} =1.00$                $n _d = 2.42$
For total internal reflection to occur, the incidence angle must be greater than the critical angle.
Critical angle  of diamond     $\theta = sin^{-1} \bigg( \dfrac{n _a}{n _d} \bigg)$ $= sin^{-1} \bigg( \dfrac{1.00}{2.42} \bigg)  = 24^o$
Thus the smallest angle for total internal reflection to occur in diamond is  $24^o$.
Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

The critical angle for a medium with respect to air is $45^o$. The refractive index of that medium with respect to air is

  1. $\dfrac{\sqrt 3}{2}$
  2. $\dfrac{2}{\sqrt 3}$
  3. $\sqrt 2$
  4. $\dfrac{1}{\sqrt 2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Critical angle $\theta _c=45^o$

For total internal reflection 
$n _{medium}sin\theta _c=n _{air}$ , the refractive index of air is 1
$n _{medium}sin\theta _c=1$
$n _{medium}=\dfrac{1}{sin45}=\sqrt{2}$

Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

A green light is incident from the water to the air - water interface at the critical angle ($\theta$). Select the correct statement.

  1. The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.

  2. The entire spectrum of visible light will come out of the water at various angles to the normal.
  3. The entire spectrum of visible light will come out of the water at an angle of $90^o$ to the normal.

  4. The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As frequency of visible light increases refractive index increases. With the increase of refractive index critical angle decreases. So that light having frequency greater than green will get total internal reflection and the light having frequency less than green will pass to air.

Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

A glass cube of refractive index $1.5$ and edge $1cm$ has tiny black spot at its center. A circular dark sheet is to be kept symmetrically on the top surface so that the central spot is not visible from the top.Minimum radius of the circular sheet should be (Given $\dfrac{1}{\sqrt{2}}=0.707,\dfrac{1}{\sqrt{3}}=0.577,\dfrac{1}{\sqrt{5}}=0.447)$

  1. $0.994cm$
  2. $0.447cm$
  3. $0.553cm$
  4. $0.577cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$r\sin i=1.\sin 90^o$

$\sin i=\dfrac{1}{r}=\dfrac{2}{3}$

$\tan (90-i)=\dfrac{1}{2x}$

$\cot i =\dfrac{1}{2x}$

$\dfrac{\sqrt{3^2-2^2}}{x}=\dfrac{1}{2x}=D$

$x=\dfrac{1}{\sqrt{5}}=0.447 cm$
Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

A vertical pencil of rays comes from bottom of a tank filled with a liquid. When it is accelerated with an acceleration of 7.5 m/s$^2$, the ray is seen to be totally reflected by liquid surface. What is minimum possible refractive index of liquid?

  1. slightly greater than 4/3

  2. slightly greater than 5/3

  3. slightly greater than 1.5

  4. slightly greater than 1.75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$tan\theta=a/g=37^o\Rightarrow \theta _c<37^o $


$sin\theta _c=sin 37\Rightarrow \mu>5/3$

Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

If a ray of light passes from a denser medium to a rarer medium in a straight line, the angle of incidence must be ______

  1. $0^o$
  2. $30^o$
  3. $60^o$
  4. $90^o$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When light travels from one medium to another, it only continues in a straight line without refraction if the angle of incidence is 0 degrees (normal incidence).

Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

If the critical angle for the medium of prism is $C$ and the angle of prism is $A$, then there will be no emergent ray when-

  1. $A< 2C$
  2. $A=2C$
  3. $A> 2C$
  4. $A\ge 2C$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let $r _1$ be the angle of refraction at first face
and $r _2$ be the angle of refraction at second face.
as $r _1+r _2=A$
 thus, $r _1+r _2>2C.$
 This is possible if $r _2>C$
 ( as if $r _1>C$ incident ray would not enter the prism). 
$r _2>C$ implies no emergent ray.
Hence, Option $C$ is correct.
Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

A ray of light traveling in a transparent medium falls on a surface separating the medium from air, at an angle of $ { 45 }^{ \circ  }$. The ray undergoes total internal reflection. if 'n' is the refractive index of the medium with respect to air, select the possible values of 'n' from the following.

  1. 1.3

  2. 1.4

  3. 1.5

  4. 1.6
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

The angle of incidence of all the rays is $ { 45 }^{ \circ  }$ at the hypotenuse. For a critical angle of $ { 45 }^{ \circ  }$, the refractive index must be 
$ { \left( \sin { { 45 }^{ \circ  } }  \right)  }^{ -1 }=\sqrt { 2 } =1.414$

Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

When ray of light enters from one medium to another its velocity in second medium becomes double. the maximum value of angle of incidence so that total internal reflection may not take place will be

  1. $ { 60 }^{ \circ }$
  2. $ { 180 }^{ \circ }$
  3. $ { 90 }^{ \circ }$
  4. $ { 30 }^{ \circ }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Velocity becomes double so $\mu _{r}=2$


critical angle is $sin^{-1}\dfrac{1}{\mu _{r}}=sin^{-1}\dfrac{1}{2}=30^{\circ}$.

Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

The speed of light in two media  I and II are $2.2\times 10^8 m/s$ and $ 2.4\times { 10 }^{ 8 }{ m }/{ s }$ respectively. The critical angle for light refracting from I to II medium will be

  1. $\sin^{-1}( { \frac { 12 }{ 11 } } )$
  2. $ \sin^{-1} ({ \frac { 11 }{ 12 } } )$
  3. $ \sin^{-1} ({ \frac { 12 }{ 24 } } )$
  4. $ \sin^{-1}( { \frac { 12 }{ 21 } }) $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\mu _{r}=\dfrac{2.4}{2.2}$


critical angle is $sin^{-1}\dfrac{1}{\mu _{r}}=sin^{-1}\dfrac{11}{12}$