In the figure, what is the smallest incident angle θi for the beam of a particular wavelength to

In the figure, what is the smallest incident angle θi for...

In the figure, what is the smallest incident angle $\theta_{i}$ for the beam of a particular wavelength to undergo total internal reflection at the surface of the prism having an index of refraction for this wavelength of $1.5 ?$

Key Concepts

Total Internal Reflection

Total internal reflection is an optical phenomenon that occurs when a light ray travelling within a medium strikes an interface with a less optically dense medium at an angle greater than a certain threshold, causing the light to be completely reflected back into the original medium rather than refracting into the second medium.

Critical Angle

The critical angle is the minimum angle of incidence in the denser medium at which total internal reflection occurs. It is determined by the indices of refraction of the two media and establishes the boundary condition beyond which no refracted ray exists and all light is reflected.

Snell's Law

Snell's Law describes the relationship between the angles of incidence and refraction when light passes from one medium into another. It is fundamental in deriving the expression for the critical angle, as it relates the sine of the incidence angle to the sine of the refraction angle with respect to the indices of refraction of the two media.

Transcript

00:01 Hi, we have a prism made of glass with refractive index 1 .5 and it is surrounded by air.

00:07 There is an incident light coming in, heating this surface and entering the prism.

00:14 Now our task is to calculate the smallest incident angle teta i here for the beam that undergoes total internal reflection inside of the prism.

00:25 And again the prism has index of refraction of for this wavelength 1 .5.

00:30 So we need to first understand what is this theta critical angle inside of the prism.

00:36 Let's calculate that.

00:37 So for that we have the formula sign of this critical angle should be equal to the refractive index of the air divided the refractive index of the glass, which is for the air we have one.

00:58 For the glass we have 1 .5.

01:01 We have here a 0 .5.

01:03 667 approximately so the critical angle then would be inverse sign of 0 .667 we have about 42 degree.

01:18 Now this means this theta c angle is 42 degree.

01:22 Now we need to understand how can we relate that and calculate the incident angle outside.

01:28 So for that we have another diagram here.

01:32 So let's let's pay closer attention.

01:34 To what is happening.

01:36 We are given that this angle here is 70 degree.

01:39 If we think of the normal to this surface, which is this black dotted line, then if this is 70 degree, this is 90 degree, this is 20 degree.

01:49 But this is the normal to this surface, which is 90 degree, which means 90 minus 20, we have this angle also 70 degree.

01:58 Now, if we think of the other normal to this surface, this dotted line, that with this green line makes 90 degree, which means if this is 70 degree, this is also 20 degree...

Please give Ace some feedback