Discuss the refraction through a rectangular glass slab and show that the emergent ray is parallel to the incident ray but laterally displaced. How does lateral displacement depend on the thickness of the glass slab?
Or
With the help of a ray diagram, show that when light falls obliquely on a side of rectangular slab, the emergent ray is parallel to the incident ray.
Show the lateral displacement of the ray on the diagram.

Solution

Refraction through a rectangular glass slab:

Consider a rectangular glass slab PQRS, as shown in figure below. On the face PQ, a ray AB is incident at an angle of incidence i₁. It bends towards the normal, on entering the glass slab, and travels along BC inclined at an angle of refraction r₁. The refracted ray BC is incident on the face SR at an angle of incidence i₂. The emergent ray CD bends away from the normal at an angle of refraction r₂.

Now, using Snell’s law, we have
Refraction from air to glass at face PQ,

   $\frac{\sin i_{1}}{\sin r_{1}} = \frac{n_{g}}{n_{a}}$ ...(1)

where,
n_a is the refractive index of sir and
n_g is the refractive index of glass.

Fig. Refraction through a glass slab

Using Snell’s law for refraction from glass to air at face SR, we have

$\frac{\sin i_{2}}{\sin r_{2}} = \frac{n_{a}}{n_{g}}$

But    $i_{2} = r_{1},$

Therefore,
$\frac{\sin r_{1}}{\sin r_{2}} = \frac{n_{a}}{n_{g}}$ ...(2)

Multiplying equations (1) and (2), we get

$\frac{\sin i_{1}}{\sin r_{1}} \times \frac{\sin r_{1}}{\sin r_{2}} = 1$

$\Rightarrow$ $\sin i_{1} = \sin r_{2}$

i.e.,    $i_{1} = r_{2}$

Thus, the emergent ray CD is parallel to the incident ray AB, but it has been laterally displaced by a perpendicular distance CN with respect to the incident ray. This lateral shift in the path of light on emerging from a medium with parallel faces is called lateral displacement.

It is found that the lateral displacement is directly proportional to the thickness of the glass slab.

Some More Questions From Acids, Bases and Salts Chapter

Which type of phenomenon (reflection or refraction) occurs when light falls on (i) a highly polished surface like a mirror and (ii) a transparent medium like glass or water?

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For Daily Free Study Material Join wiredfaculty

Acids, Bases And Salts

Some More Questions From Acids, Bases and Salts Chapter

Define a ray of light and a beam light. What are the different types of beams of light?

What is an optical medium? How can we classify different media on the basis of their behaviour towards light?

What do you mean by reflection, refraction and absorption of light?

Which type of phenomenon (reflection or refraction) occurs when light falls on (i) a highly polished surface like a mirror and (ii) a transparent medium like glass or water?

What is meant by the optical image of an object?

What are real and virtual images? Can these images be obtained on a screen? Give reasons in support of your answer.

Give three points of differences between real and virtual images.

What is a mirror? Mention the different types of mirrors commonly used.

Define the following terms in connection with reflection of light:Incident ray, reflected ray, point of incidence, normal, angle of incidence and angle of reflection.

State the laws of reflection of light.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Define the following terms in connection with reflection of light:
Incident ray, reflected ray, point of incidence, normal, angle of incidence and angle of reflection.