Refraction in a Glass Slab

Concept Explanation

Refraction in a Glass Slab

Refraction of Light:

It is a process of bending of light ray when passing from one medium to another.This bending of light depends not only on the the refractive indices of the two media but also depends on the angle of incidence.

Refraction in a Glass Slab:

Suppose a ray of light AB traveling through air with refractive index ( $eta$ = 1 ) incident at an $large angle i_1$ (angle of incidence) on the upper surface of a transparent rectangular slab. This ray gets refracted by an $large angle r_1$ (angle of refraction) at the upper surface and moves along BC known as refracted ray.

As the ray of light travels from air (rarer medium) to the glass slab (denser medium) therefore it bends towards the normal which means that $large angle i_1> angle r_1$ .

According to Snell's law

$large frac{sin;i_1}{sin;r_1}=frac{eta_{glass}}{eta_{air}}$ .......[ I ]

When the refracted ray ,BC reaches the lower surface SR,. is incident at an $large angle i_2$ (angle of incidence) . This ray gets refracted by an $large angle r_2$ (angle of refraction) This refracted ray that comes out of the glass slab is known emergent ray. In this case light ray travels from glass slab (denser medium) to the air (rarer medium) and bends away from the normal which means $large angle r_2> angle i_2$ .

According to Snell's law

$large frac{sin;i_2}{sin;r_2}=frac{eta_{air}}{eta_{glass}}$ .......[ II ]

The two surfaces PQ and RS are parallel to each other so the normal at the two surface are also parallel to each other. and BC is the transversal cutting them so

$large angle r_1= angle i_2$ ................[ III ] [Alternate angles]

From II and III we get

$large frac{sin;r_1}{sin;r_2}=frac{eta_{air}}{eta_{glass}}$

Taking the reciprocal we get

$large frac{sin;r_2}{sin;r_1}=frac{eta_{glass}}{eta_{air}}$ .......[ IV ]

From Equation I and IV we get

$large frac{sin;r_2}{sin;r_1}=frac{sin; i_1}{sin;r_1}$

$large Rightarrow sin;r_2=sin; i_1$

$large Rightarrow r_2= i_1$

But they are corresponding angles, as they are equal so we can say that the incident ray is parallel to emergent ray but is laterally didsplaced.This lateral distance between the incident ray and emergent ray is known as lateral displacement.

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Sample Questions

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Question : 1

In the case of glass slab the lateral displacement it depends on the following factors like .
A. Refractive index of the medium	B. Thickness of the medium	C. Angle of incidence	D. All of these .
Right Option : D
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Question : 2

In a rectangular glass slab , if the incident angle is i and emergent angle is e, which of the following relations between i and e is true ?
A. i>e	B. i	C. i=e	D. i
Right Option : C
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Question : 3

In the case of glass slab the ray after refraction at the upper surface and moves inside the glass slab and is known as _________________ .
A. Incident ray	B. Refracted ray	C. Emergent ray	D. None of these .
Right Option : B
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