Tag: physics

Questions Related to physics

An optical fiber ($\mu=1.72$) has a coating of glass ($\mu=1.5$). The critical angle for total internal reflection is

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

  1. $ { sin }^{ -1 }\left( \dfrac { 75 }{ 86 } \right) $

  2. $ { sin }^{ -1 }\left( \dfrac { 86 }{ 75 } \right) $

  3. $ { sin }^{ -1 }\left( 0.8 \right) $

  4. $ { sin }^{ -1 }\left( 0.82 \right) $

Show answer
Correct Option: A
Explanation:

The critical angle for total internal reflection is given as $sin\theta _c=\dfrac{\mu _2}{\mu _1}$, where $\mu _1$ is the refractive index of the denser medium.
Thus we get 


$sin\theta _c=\dfrac{1.5}{1.72}$

or  $\theta _c=sin^{-1}\dfrac{75}{86}$.

If the refractive index of water is 4/3 and that of glass is 5/3, then the critical angle of light entering from glass into water will be

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

  1. $ \sin^{-1} ({ \dfrac { 4 }{ 5 } } )$

  2. $ \sin^{-1} ({ \dfrac { 3 }{ 4 } }) $

  3. $ \sin^{-1} ({ \dfrac { 1 }{ 2 } } )$

  4. $ \sin^{-1} ({ \dfrac { 2 }{ 3 } }) $

Show answer
Correct Option: A
Explanation:
When a light ray travels from denser to rarer medium, then the angle of incidence for which the refracted ray becomes parallel to the interface$( \angle r = 90^{\circ} )$, is known as critical angle for that pair of media. 
Here, the denser medium is Glass $ \mu _g = \dfrac{5}{3} $
&
the rarer medium is water $ \mu _w = \dfrac{4}{3} $

Applying Snell's law at the interface of the two media, we have
$ \mu _g \times Sin\ i _c = \mu _w \times Sin\ r $

From definition, we know, 
$ \angle r = 90^{\circ} $

$ \Rightarrow \mu _g \times Sin\ i _c = \mu _w \times Sin\ 90^{\circ} $

$ \Rightarrow \dfrac{5}{3} \times Sin\ i _c =  \dfrac{4}{3} $
$  \Rightarrow Sin\ i _c = \dfrac{\Big( \dfrac{4}{3} \Big) }{\Big( \dfrac{5}{3} \Big)} $

$  \Rightarrow Sin\ i _c = \dfrac{4}{5} $

$  \Rightarrow i _c = Sin^{-1} \Big( \dfrac{4}{5} \Big) $ 


Hence, the correct answer is OPTION A.

The velocity of light in a medium is half its velocity in air. If a ray of light emerges from such a medium into air, the angle of incidence, at which it will be totally internally reflected, is

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

  1. $15^o$

  2. $30^o$

  3. $45^o$

  4. $60^o$

Show answer
Correct Option: B
Explanation:

max angle is critical angle , velocity is halved hence $\mu _{r}=2$


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

option $B$ is correct 

A ray of light traveling in glass $(\mu=3/2)$ is incident on a horizontal glass-air surface at the critical angle $\theta _C$. If a thin layer of water $(\mu =4/3)$ is now poured on the glass-air surface, the angle at which the ray emerges into air at the water-air surface is

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

  1. $60^o$

  2. $45^o$

  3. $90^o$

  4. $180^o$

Show answer
Correct Option: C
Explanation:

critical angle is $sin^{-1}\dfrac{1}{\mu _{r}}=sin^{-1}\dfrac{2}{3}$
apply Snell's law at all boundaries

$\mu _{1}sin\alpha _{1}=\mu _{2}sin\alpha _{2}=\mu _{3}sin\alpha _{3}$ 

$\dfrac{3}{2}sin \theta _{c}=1 \times sin\theta$

$\theta=90$, hence option $C$ is correct 

A ray of light from a denser medium strikes a rarer medium at an angle of incidence $i$. The reflected and refracted rays make an angle of $\pi/2$ with each other. If the angles of reflection and refraction are $r$ and $r'$, then the critical angle will be

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

  1. $\tan^{-1}(\sin i)$

  2. $\sin^{-1}(\sin r)$

  3. $\sin^{-1}(\tan i)$

  4. $\sin^{-1}(\tan r)$

Show answer
Correct Option: C
Explanation:
as the reflected and refracted rays are 90 then the angle of refraction is $90-i$

according to Snell's law
$sini\mu _{r}=sin(90-i)$

$\mu _{r}=coti$

critical angle is $sin^{-1}\dfrac{1}{\mu _{r}}=sin^{-1}\dfrac{1}{coti}=sin^{-1}tani$
option $C$ is correct 

A fish looks upward at an unobstructed overcast sky. What total angle does the sky appear to subtend? (Take refractive index of water is $\sqrt 2)$

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

  1. $180^o$

  2. $90^o$

  3. $75^o$

  4. $60^o$

Show answer
Correct Option: B
Explanation:
as the refractive index is $\sqrt{2}$ the critical angle is $sin^{-1}\dfrac{1}{\mu _{c}}=sin^{-1}\dfrac{1}{\sqrt{2}}=45^{\circ}$

 total angle the sky appear to subtend is $2\times 45 =90^{\circ}$

option $B$ is correct 

A ray of light traveling in a transparent medium falls on a surface separating the medium from air at an angle of incidence of $45^o$. The ray undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value(s) of n from the following

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

  1. 1.3

  2. 1.4

  3. 1.5

  4. 1.6

Show answer
Correct Option: C,D
Explanation:

$\mu _{min}=\dfrac{1}{sin45}=\sqrt{2}=1.414$


possible values of $\mu$ are $1.5$ and $1.6$ 

option $C,D$ are correct 

The critical angle for glass-air is $45^o$ for the light of yellow colour. State whether it will be less than, equal to, or more than $45^o$ for  blue light?

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

  1. more than $45^o$

  2. less than $45^o$

  3. same as $45^o$

  4. cant say

Show answer
Correct Option: B
Explanation:

According to Snell's Law: $\dfrac{sin i _c}{sin r}=\dfrac{n _2}{n _1}$ and for critical angle of incidence $r=90^o$ and $n _2=1$


Blue light has higher refractive index than yellow light hence it's critical angle will be lower than yellow light.

The critical angle for glass-air is $45^o$ for the light of yellow colour. State whether it will be less than , equal to, or more than $45^o$ for  red light?

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

  1. more than $45^o$

  2. less than $45^o$

  3. same as $45^o$

  4. can't say

Show answer
Correct Option: A
Explanation:

According to Snell's Law: $\dfrac{sin i _c}{sin r}=\dfrac{n _2}{n _1}$ and for critical angle of incidence $r=90^o$ and $n _2=1$


Red light has lower refractive index than yellow light hence it's critical angle will be higher than yellow light.

State the approximate value of the critical angle for (a) glass-air surface, (b) water-air surface (Given $\mu _{glass} =1.5, \mu _{water}=1.33$)

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

  1. (a) $49^o$, (b)$49^o$

  2. (a) $42^o$, (b)$42^o$

  3. (a) $42^o$, (b)$49^o$

  4. (a) $49^o$, (b)$42^o$

Show answer
Correct Option: C
Explanation:

Critical angle is the angle of incidence from denser to rarer medium for which the angle of refraction is $%%90^o$
These angles for glass-air interface is $42^o$ and water-air interface is $49^o$