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Corrected example of mercury as liquid
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Koustubh Jain
Koustubh Jain
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I was studying geometrical optics the other day and my teacher told me about the concept of critical angle and total internal reflection.

He had taken an example in which a beaker was filled with a liquid whose refractive index was $\mu$ and above the beaker after some gap was the eye of an observer in the air (refractive index = 1). And an object was placed at the bottom of the beaker.

NOTE: $\mu > 1$

rough diagram

I know that for $\angle~i>\angle~i_c$ the boundary of the medium(i.e. the liquid in this case) behaves like a plane mirror and the incident rays just reflect back into the medium.

But If we take into account the meniscus of the liquid at the surface, say it is mercury then it will havesome transparent liquid which has a convex meniscus, so won't the surface behave like a spherical mirror for $\angle~i>\angle~i_c$ ?

I was studying geometrical optics the other day and my teacher told me about the concept of critical angle and total internal reflection.

He had taken an example in which a beaker was filled with a liquid whose refractive index was $\mu$ and above the beaker after some gap was the eye of an observer in the air (refractive index = 1). And an object was placed at the bottom of the beaker.

NOTE: $\mu > 1$

rough diagram

I know that for $\angle~i>\angle~i_c$ the boundary of the medium(i.e. the liquid in this case) behaves like a plane mirror and the incident rays just reflect back into the medium.

But If we take into account the meniscus of the liquid at the surface, say it is mercury then it will have a convex meniscus, so won't the surface behave like a spherical mirror for $\angle~i>\angle~i_c$ ?

I was studying geometrical optics the other day and my teacher told me about the concept of critical angle and total internal reflection.

He had taken an example in which a beaker was filled with a liquid whose refractive index was $\mu$ and above the beaker after some gap was the eye of an observer in the air (refractive index = 1). And an object was placed at the bottom of the beaker.

NOTE: $\mu > 1$

rough diagram

I know that for $\angle~i>\angle~i_c$ the boundary of the medium(i.e. the liquid in this case) behaves like a plane mirror and the incident rays just reflect back into the medium.

But If we take into account the meniscus of the liquid at the surface, say some transparent liquid which has a convex meniscus, so won't the surface behave like a spherical mirror for $\angle~i>\angle~i_c$ ?

improved formatting
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Koustubh Jain
Koustubh Jain
  • 296
  • 1
  • 2
  • 23

I was studying geometrical optics the other day and my teacher told me about the concept of critical angle and total internal reflection.

He had taken an example in which a beaker was filled with a liquid whose refractive index was $\mu$ and above the beaker after some gap was the eye of an observer in the air (refractive index = 1). And an object was placed at the bottom of the beaker.

NOTE: $\mu > 1$

rough diagram

I know that for $\angle~i>\angle~i_c$ the boundary of the medium(i.e. the liquid in this case) behaves like a plane mirror and the incident rays just reflect back into the medium.

But If we take into account the meniscus of the liquid at the surface, say it is mercury then it will have a convex meniscus, so won't the surface behave like a spherical mirror for $\angle~i>\angle~i_c$ ?

I was studying geometrical optics the other day and my teacher told me about the concept of critical angle and total internal reflection.

He had taken an example in which a beaker was filled with a liquid whose refractive index was $\mu$ and above the beaker after some gap was the eye of an observer in the air (refractive index = 1). And an object was placed at the bottom of the beaker.rough diagram

I know that for $\angle~i>\angle~i_c$ the boundary of the medium(i.e. the liquid in this case) behaves like a plane mirror and the incident rays just reflect back into the medium.

But If we take into account the meniscus of the liquid at the surface, say it is mercury then it will have a convex meniscus, so won't the surface behave like a spherical mirror for $\angle~i>\angle~i_c$ ?

I was studying geometrical optics the other day and my teacher told me about the concept of critical angle and total internal reflection.

He had taken an example in which a beaker was filled with a liquid whose refractive index was $\mu$ and above the beaker after some gap was the eye of an observer in the air (refractive index = 1). And an object was placed at the bottom of the beaker.

NOTE: $\mu > 1$

rough diagram

I know that for $\angle~i>\angle~i_c$ the boundary of the medium(i.e. the liquid in this case) behaves like a plane mirror and the incident rays just reflect back into the medium.

But If we take into account the meniscus of the liquid at the surface, say it is mercury then it will have a convex meniscus, so won't the surface behave like a spherical mirror for $\angle~i>\angle~i_c$ ?

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Koustubh Jain
Koustubh Jain
  • 296
  • 1
  • 2
  • 23

Will the medium boundary act like a spherical mirror?

I was studying geometrical optics the other day and my teacher told me about the concept of critical angle and total internal reflection.

He had taken an example in which a beaker was filled with a liquid whose refractive index was $\mu$ and above the beaker after some gap was the eye of an observer in the air (refractive index = 1). And an object was placed at the bottom of the beaker.rough diagram

I know that for $\angle~i>\angle~i_c$ the boundary of the medium(i.e. the liquid in this case) behaves like a plane mirror and the incident rays just reflect back into the medium.

But If we take into account the meniscus of the liquid at the surface, say it is mercury then it will have a convex meniscus, so won't the surface behave like a spherical mirror for $\angle~i>\angle~i_c$ ?