Question

A ray of light travelling through air falls on the surface of a glass slab and emerges out of it parallel to the incident ray. The angle of incidence i, angle of refraction in glass r and angle of emergence is e. Find the ratio of sin i/sin e and refraction index of glass in terms of e and r

Answer 1

Explanation:

When a beam of light falls obliquely at the interface of the two optical media, direction of its path changes when it enters into the other medium. This phenomenon exhibited by the light rays is called refraction of light. This is due to the change in speed of light while going from one medium to the other.

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During the refraction, when light travels from one medium to another transparent medium, the speed and wavelength of light changes, whereas frequency remains the same.

When a light ray travels from rarer to denser medium, its speed gets slow down and the ray bends towards normal (∠i >∠r).

When the ray of light travels from denser to rarer medium, its speed goes up and the ray bends away from the normal (∠i < ∠r).

From the above two points, we can conclude that the light bends on undergoing refraction.

Laws of Refraction:

At the point of incidence the incident ray, the refracted ray and the normal to the interface, all lie in the same plane.

The ratio of the sine of angle of incidence to the sine of angle of refraction is constant for the same colour of light and for the same pair of transparent media. Thus,

sin i/sin r = constant = n21

Where n21 is called the refractive index of the second medium with respect to first medium.

This law is also known as Snell’s law of refraction.

Refraction through rectangular glass slab with parallel faces:

The refraction takes place at both air-glass interface and glass-air interface has the following characteristics:

When a light ray travels from air to glass, the angle of incidence is greater than angle of refraction as ray bends towards normal.

When a light ray travels from glass to air, the angle of refraction (also called angle of emergent in case of glass) is greater than the angle of incidence of glass-air interface as ray of light bends away from the normal.

If the angle of incidence is zero, i.e. the incident ray is normal to the interface, the ray of light continues to travel in the same direction after refraction.

The angle of emergence and angle of incidence will be equal.

Emergent ray is parallel to the incident ray along with original direction but it will be laterally displaced to the left of the incident ray.

For the same angle of incidence, lateral displacement is proportional to the thickness of the glass slab.

For the same thickness of glass slab, the lateral displacement is proportional to the angle of incidence.

Answer 2

The ratio of sin i/sin r is 1

Refractive index of the glass in terms of e and r is = sin e/sin r

Explanation:

If the refractive index of the glass slab is n then

by Snell's law

$n=\frac{\sin i}{\sin r}$   .......... (1)

Since both the normals are parallel therefore, the alternate angles will be equal

Therefore, $\theta=r$

Again when ray of light enters from glass slab to air

$\frac{1}{n}=\frac{\sin r}{\sin e}$   ......... (2)

Multiplying (1) and (2)

$n\times\frac{1}{n}=\frac{\sin i}{\sin r}\times \frac{\sin r}{\sin e}$

$\implies 1=\frac{\sin i}{\sin e}$

or, $\frac{\sin i}{\sin e}=1$

From (2)

Refractive index of glass in terms of e and r

$n=\frac{\sin e}{\sin r}$

Hope this answer is helpful.

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