The critical angle of light going from medium A into medium B is \$\theta \$ . If the speed of light in medium A is \$v\$, then the speed of light in medium B is :

For total internal reflection \$n_{A} sin \theta =n_{B}\$when \$n_{A}=\$ refractive index of medium A\$n_{B}=\$ refractive index of medium B\$\dfrac{n_{A}}{n_{B}}=\dfrac{1}{sin \theta}\$by snell's law \$\dfrac{n_{A}}{n_{B}}=\dfrac{v_{B}\left ( velocity \ in \ medium \ B \right )}{v_{A}(velocity \ in \ medium \ A)}\$\$\dfrac{v_{B}}{v_{A}}=\dfrac{1}{sin \theta}\$\$v_{B}=\dfrac{v_{A}}{sin \theta}\$\$=\dfrac{v}{sin \theta}\$

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Prism binoculars

Q: A silicon optical fibre with a core diameter large enough has a core refractive index of 1.50 and a cladding refractive index 1.47. Determine(i) the critical angle at the core cladding interface,(ii) the numerical aperture for the fibre(iii) the acceptance angle in air for the fibre.

Here,\${ \mu }_{ 1 }=1.50;{ \mu }_{ 2 }=1.47;\$\${ \mu }_{ 0 }=1\$(i) Critical angle \${ \theta }_{ c }\$ at the core-cladding interface is given by \${ \theta }_{ c }={ sin }^{ -1 }\dfrac { 1.47 }{ 1.50 } =78.{ 5 }^{ 0 }\$(ii) Numerical aperture,\$NA={ \left( { { \mu }_{ 1 } }^{ 2 }-{ { \mu }_{ 2 } }^{ 2 } \right) }^{ \frac { 1 }{ 2 } }\$ \$={ \left[ { \left( 1.50 \right) }^{ 2 }-{ \left( 1.47 \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }={ \left( 2.25-2.16 \right) }^{ 1/2 }=0.30\$(iii) Acceptance angle \${ \theta }_{ a }={ sin }^{ -1 }\left( NA \right) \$\$={ sin }^{ -1 }\left( 0.30 \right) ={ 17.4 }^{ 0 }\$

Q: A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12cm below the surface, the radius of this circle (in cm) is:

\$\displaystyle \sin i_{c}=\frac{1}{\mu}=\frac{r}{\sqrt{r^{2}+h^{2}}}\$Using \$h=12\$ cm, \$\mu=4/3\$We get \$\displaystyle r=\frac{36}{\sqrt{7}}\$ cm.

Q: The refractive index of the material of a prism is \$\sqrt{2}\$ and the angle of the prism is \$30^o\$. One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is?

Using \$ A = r_{1} + r_{2}\$\$ 30 = r_{1} + 0\$so \$r_{1} = 30\$Using Snell's Law, \$ 1 \times sin i = \mu \times sin r\$\$ 1 \times sin i = \sqrt{2} \times sin 30 = \sqrt{2} 3/2\$\$sin i = 1/ \sqrt{2}\$\$ i = 45^{o}\$option 4 is correct

Q: Mention three applications of total internal reflection of light.

Total internal reflection can be applied in the following:1. Telecommunication systems2. Automotive rain sensors and windscreen wipers3. Optical fingerprinting devices

Q: What are the necessary conditions for total internal reflection to take place?

For total internal reflection to take place (i) light must travel from a denser medium to a rarer medium and (ii) the angle of incidence inside the denser medium must be greater than the critical angle. i.e., \$\angle i > \angle c\$.

Q: A ray of light travelling in a transparent medium of refractive index \$\mu\$, falls on a surface separating the medium from air at an angle of incidence of \$45^o\$ . For which of the following value of \$\mu\$ the ray can undergo total internal reflection ?

For total internal reflection, sin i > sin c where, i = angle of incidence, C = critical angle But, \$sin \, C \, = \, \dfrac{1}{\mu} \,\, \therefore \, sin \, i \, = \, \dfrac{1}{\mu} \,\, or \,\, \mu \, = \, \dfrac{1}{sin \, i}\$\$\therefore \, \mu \, > \, \dfrac{1}{sin \, 45} \,\, or \,\, \mu \, > \, \sqrt 2 \,\, (i \, = \, 45 \, Given)\$Hence, option (c) is correct.

Q: A ray of light is incident at the glass-water interface at an angle \$i\$. It merges finally parallel to the surface of the water. Then, the value of \$\mu_{g}\$ would be(where \$\mu_{g}\$ is the refractive index of glass with respect to water)

Applying Snell's law at glass-water surface,\$_{g}^{w}\mu = \dfrac {\sin r}{\sin i} = \dfrac {_{g}\mu}{_{w}\mu} ... (i)\$Applying Snell's law at water-air surface,\$_{w}^{a}\mu = \dfrac {\sin 90^{\circ}}{\sin r} = \dfrac {_{w}\mu}{_{a}\mu} ... (ii)\$Multiplying (i) and (ii),\$\dfrac {_{g}\mu}{_{a}\mu} = \dfrac {1}{\sin i}\ \Rightarrow _{g}\mu = \dfrac {1}{\sin i}\$.

Q: A transparent solid cylindrical rod has a refractive index of \$\displaystyle \dfrac{2}{\sqrt{3}}\$. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle \$\theta\$ for which the light ray grazes along the wall of the rod is -

\$ \displaystyle I\times \sin90 = \frac{2}{\sqrt{3}}\sin(90-\alpha)\$\$\Rightarrow \displaystyle \cos\alpha=\frac{\sqrt{3}}{2}\$So, \$\displaystyle \sin\alpha=\sqrt{1-\frac{3}{4}}=\frac{1}{2}\$Now, \$ 1\displaystyle \times\sin\theta=\frac{2}{\sqrt{3}}\sin\alpha=\displaystyle \frac{2}{\sqrt{3}}\times\frac{1}{2}=\frac{1}{\sqrt{3}}\$\$\Rightarrow \theta =\displaystyle \sin^{-1}\frac{1}{\sqrt{3}}\$

Physics

example

Periscope

Periscopes are used in order to see the objects that are not in direct line of sight. Its working is based on the laws of reflection. It consists of a set of parallel plane mirrors as shown in the diagram.

result

Total internal reflecting prism as a plane mirror

Image formed by total reflecting prism is brighter than a plane mirror because all of the incident light is reflected. It is used to deviate light by

9 0^{o}

in periscope and

18 0^{o}

in binoculars.

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Total Internal Reflection and Critical angle

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Applications of Total Internal Reflection

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Periscope

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Total Internal Reflection Through Prism

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Some Standard Conceptual Questions on TIR

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Important Questions

A silicon optical fibre with a core diameter large enough has a core refractive index of 1.50 and a cladding refractive index 1.47. Determine
(i) the critical angle at the core cladding interface,
(ii) the numerical aperture for the fibre
(iii) the acceptance angle in air for the fibre.

Medium

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A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12cm below the surface, the radius of this circle (in cm) is:

Medium

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The refractive index of the material of a prism is $2$ and the angle of the prism is $3 0^{o}$ . One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is?

Medium

NEET

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Mention three applications of total internal reflection of light.

Easy

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What are the necessary conditions for total internal reflection to take place?

Medium

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A ray of light travelling in a transparent medium of refractive index $μ$ , falls on a surface separating the medium from air at an angle of incidence of $4 5^{o}$ . For which of the following value of $μ$ the ray can undergo total internal reflection ?

Medium

View solution

A ray of light is incident at the glass-water interface at an angle $i$ . It merges finally parallel to the surface of the water. Then, the value of $μ_{g}$ would be(where $μ_{g}$ is the refractive index of glass with respect to water)

Medium

JEE Advanced

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A transparent solid cylindrical rod has a refractive index of $\frac{2}{3}$ . It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $θ$ for which the light ray grazes along the wall of the rod is -

Hard

JEE Mains

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Define critical angle. Explain total internal reflection using a neat diagram.

Medium

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The critical angle of light going from medium A into medium B is $θ$ . If the speed of light in medium A is $v$ , then the speed of light in medium B is :

Medium

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example

Periscope

result

Total internal reflecting prism as a plane mirror

REVISE WITH CONCEPTS

Total Internal Reflection and Critical angle

Optical Fibres

Critical Angle - Formula

Applications of Total Internal Reflection

Quick Summary With Stories

Periscope

Some Standard Conceptual Questions on TIR

A silicon optical fibre with a core diameter large enough has a core refractive index of 1.50 and a cladding refractive index 1.47. Determine (i) the critical angle at the core cladding interface, (ii) the numerical aperture for the fibre (iii) the acceptance angle in air for the fibre.

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12cm below the surface, the radius of this circle (in cm) is:

Mention three applications of total internal reflection of light.

What are the necessary conditions for total internal reflection to take place?

A ray of light travelling in a transparent medium of refractive index μ, falls on a surface separating the medium from air at an angle of incidence of 45o . For which of the following value of μ the ray can undergo total internal reflection ?

A ray of light is incident at the glass-water interface at an angle i. It merges finally parallel to the surface of the water. Then, the value of μg​ would be(where μg​ is the refractive index of glass with respect to water)

A transparent solid cylindrical rod has a refractive index of 3​2​. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle θ for which the light ray grazes along the wall of the rod is -

Define critical angle. Explain total internal reflection using a neat diagram.

The critical angle of light going from medium A into medium B is θ . If the speed of light in medium A is v, then the speed of light in medium B is :

A silicon optical fibre with a core diameter large enough has a core refractive index of 1.50 and a cladding refractive index 1.47. Determine
(i) the critical angle at the core cladding interface,
(ii) the numerical aperture for the fibre
(iii) the acceptance angle in air for the fibre.

A ray of light travelling in a transparent medium of refractive index $μ$ , falls on a surface separating the medium from air at an angle of incidence of $4 5^{o}$ . For which of the following value of $μ$ the ray can undergo total internal reflection ?

A ray of light is incident at the glass-water interface at an angle $i$ . It merges finally parallel to the surface of the water. Then, the value of $μ_{g}$ would be(where $μ_{g}$ is the refractive index of glass with respect to water)

A transparent solid cylindrical rod has a refractive index of $\frac{2}{3}$ . It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $θ$ for which the light ray grazes along the wall of the rod is -

The critical angle of light going from medium A into medium B is $θ$ . If the speed of light in medium A is $v$ , then the speed of light in medium B is :