Optics Concept Page - 13

Definition

Lateral displacement

Lateral displacement is the distance between the incident ray and the emergent ray. It is given by
l=tsin(i−r)cos(r)$l=t{\displaystyle \frac{sin(i-r)}{cos(r)}}$
t:$t:$ Thickness of glass slab
i:$i:$ Angle of incidence
r:$r:$ Angle of refraction

Definition

Spherical Refracting Surface

A refracting surface, which forms a part of a sphere of transparent refracting material, is called spherical refracting surface.
The two types are convex spherical refracting surfaces and concave spherical refracting surface.

Example

Examples of refraction

Some common examples of refraction in our daily life include the formation of rainbow, blue colour of sky and oceans, reddish sun during sunrise and sunset, etc.

Definition

Multiple refraction

Now let us consider a double layer  consisting of two parallel-sided slabs of refractive indices n2 and n3$n_{2}and{n}_3$,   surrounded by a third medium of different refractive index n1$n_1$, where n1<n2<n3$n_1<n_2<n_3$ We may take medium 1 to be air (n1=1)$(n_1=1)$ medium 2 to be water (n2=1.33)$(n_2=1.33)$ and medium 3 to be glass (n)3=1.5)$(n{)}_3=1.5)$, for example.
The diagram shows the passage of a ray of light from the air through the glass and water, emerging finally into the air in the same direction.  Note that at each of the two boundary surfaces, some of the light is reflected.   
From Snell's Law, we have
n1sinθ1=n2sinθ2=n3sinθ3$n_{1}sin{\theta }_1=n_{2}sin{\theta }_2=n_{3}sin{\theta }_3$

Definition

Critical angle

When the angle of incidence in water reaches a certain critical value, the refracted ray lies along the boundary, having an angle of refraction of 90-degrees. This angle of incidence is known as the critical angle; it is the largest angle of incidence for which refraction can still occur. For any angle of incidence greater than the critical angle, light will undergo total internal reflection.

Definition: 
The angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected.

Formula

Critical angle derivation

Definition: 
The angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected.

So the critical angle is the angle of incidence that provides an angle of refraction of 90-degrees.For the water-air boundary, the critical angle is 48.6$48.6$degrees.
For the crown glass-water boundary, the critical angle is 61.0$61.0$degrees.
The actual value of the critical angle is dependent upon the combination of materials present on each side of the boundary.
Let us consider medium i −$-$ Incident medium and r −$-$ Refractive medium, Then value of critical angle can be derived by Snell's law.
nisinθi=nrsinθr$n_{i}sin{\theta }_i=n_{r}sin{\theta }_r$
nisinθcrit=nrsin90∘$n_{i}sin{\theta }_{crit}=n_{r}sin{90}^{\circ }$
sinθcrit=nrni$sin{\theta }_{crit}={\displaystyle \frac{n_r}{n_i}}$The critical angle can be calculated by taking the inverse-sine of the ratio of the indices of refraction. The ratio of nr/ni is a value less than 1.0

Definition

Total internal reflection (TIR)

Introduction: When light travels from an optically denser medium to a rarer medium at the interface, it is partly reflected back into the same medium and partly refracted to the second medium. This reflection is called the internal reflection.

Definition:
Total internal reflection is defined as the complete reflection of a light ray at the boundary of two media, when the ray is in the medium with greater refractive index.

Result

Experimental verifications of total internal reflection

Experiment 1:

• Take a glass beaker with clear water in it.
• Stir the water a few times with a piece of soap, so that it becomes a little turbid.
• Take a laser pointer and shine its beam through the turbid water.
• You will find that the path of the beam inside the water shines brightly.
• Shine the beam from below the beaker such that it strikes at the upper water surface at the other end.
• It undergoes partial reflection and partial refraction.
• Now direct the laser beam from one side of the beaker such that it strikes the upper surface of water more obliquely.
• Adjust the direction of laser beam until you find the angle for which the refraction above the water surface is totally absent.
• The beam is totally reflected back to water. This is called as total internal reflection.

Experiment 2:

• Pour the turbid water in a long test tube.
• Shine the laser light from top.
• Adjust the direction of the laser beam such that it is totally internally reflected every time it strikes the walls of the tube.
• This demonstrates total internal reflection.

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