A horizontal beam of light enters a 45^∘-90^∘-45^∘ prism at the center of its long side, as show

A horizontal beam of light enters a 45^∘-90^∘-45^∘ prism at...

A horizontal beam of light enters a $45^{\circ}-90^{\circ}-45^{\circ}$ prism at the center of its long side, as shown in Figure $26-51$. The emerging ray moves in a direction that is $34^{\circ}$ below the horizontal. What is the index of refraction of this prism?

Key Concepts

Index of Refraction

The index of refraction quantifies how much a medium slows down light compared to its speed in a vacuum. It is a key parameter in optics that determines the degree to which light is refracted when entering the medium. This concept is crucial for understanding and applying the principles of light propagation, bending, and the design of optical devices.

Prism Geometry

Prism geometry involves the study of the shape and angle configuration within a prism, which is important for understanding how light rays propagate through it. The angles of the prism’s faces and their orientation relative to the incoming light dictate the path taken by the light, which in turn determines the overall deviation or redirection of the emerging beam.

Snell’s Law

Snell’s law describes how light rays bend when transitioning between media with different refractive indices. It relates the sine of the angle of incidence in the first medium times its refractive index to the sine of the angle of refraction in the second medium. This principle is fundamental in predicting and calculating the change in direction of light as it moves from one material to another.

Transcript

00:01 Hi, here in this given problem this is an isosceles right angled prism, both the angles 45 degree.

00:16 At its midpoint a horizontal ray of light is allowed to incident like this.

00:29 Now we draw a normal at this point.

00:35 Obviously with this normal will be passing through the vertex of this prism like this.

00:55 So it is clear by the symmetry that if this angle is 45 degree, this angle of incidence will also be 45 degree.

01:07 This is the incident ray.

01:09 Now this incident ray will go will deviate towards the normal within this prism like this and then we draw one more normal over here like this and finally the ray of light will come out in the air again.

01:37 And this angle of emergence in the air that is given to be 34 degree.

01:46 So if we look at all the this angle here that will also be equal to 45 degree.

01:57 If this is 90, so this angle will also be 45 degree.

02:02 So if we consider this angle of refraction to be r and this angle for the incidence from glass to air back.

02:12 Suppose this angle is r dash, then using angle, no using external angle theorem, this r plus r dash that will be equal to external angle 45 degree means we can say r dash is equal to 45 degree minus angle r.

02:50 So using snell's law for the refraction into the prism and refractive index of the material of the prism n is equal to sin i, which is 45 degree divided by sin r.

03:24 Make it equation number 1.

03:27 Then using snell's law again but this time for the refraction out of the prism means here at the surface...

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