A ray of light of a particular wavelength is incident on an...

A ray of light of a particular wavelength is incident on an equilateral triangular prism whose index of refraction for light of this wavelength is $1.23 .$ The ray is parallel to the base of the prism as it approaches and enters the prism at the midpoint of one of the sides, as shown in the figure. What is the direction of the ray when it emerges from the prism?

Key Concepts

Prism Geometry

Prism geometry involves understanding the shape and angles of a prism, which in turn affects the path that light takes through the prism. The internal angles of the prism and the orientation of the light ray at entry determine the subsequent angles of incidence and refraction at each interface. This concept is important for analyzing and predicting the deviation of light as it passes through the prism.

Ray Path Analysis

Ray path analysis entails tracking the trajectory of a light ray as it undergoes refraction at the surfaces of optical components. By applying Snell's Law at each interface and considering the geometric configuration of the prism, one can determine the overall deviation or emerging direction of the light ray. This systematic approach is fundamental in solving problems in geometrical optics.

Snell's Law

Snell's Law is the fundamental principle governing the refraction of light at an interface between two media with different refractive indices. It relates the sine of the angle of incidence to the sine of the angle of refraction, scaled by the ratio of the refractive indices of the two media. This law is essential for analyzing how light bends as it enters or exits a material, such as a prism.

Index of Refraction

The index of refraction is a measure of how much a ray of light slows down and bends when entering a medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. This concept is crucial in determining the degree to which light rays are refracted upon entry into, and exit from, optical materials.

Transcript

00:01 Hi, we have a ray of light that is incident on an equilateral triangular prism, which has index of refraction 1 .23.

00:10 The ray is parallel to the base of the prism when approaches the present.

00:16 It is entering at the midpoint of one of its sides, so we need to find the direction of the ray when it emerges from the triangular prism.

00:29 So let's first look at the angles that we have here.

00:33 This is the equilateral triangle, so this angle is 60 degree.

00:38 If this is perpendicular to the side, this is 90 degree, which means this is 30 degree.

00:43 And from this geometry, we can see that if this is 60 degree, those are parallel, then this is also 60 degree.

00:50 And this is the normal to the side where the light ray enters.

00:55 That means we also have here 90 minus 60 which is 30 degrees so this angle with the normal of incident right is 30 degree let's try to understand what is the angle of refraction this theta r angle that is going inside of the prism so for that we are going to use smell slow n1 sign of theta 1 this is for the error is equal to n2 sign of theta 2 this is inside of the prism.

01:28 That means sine of theta 2 is equal to n1, sign of theta 1 over n2.

01:36 Now this is equal to n1 is for the air is 1 times sine of our angle 30 degree divided to the n2 is the refraction index for the prism which is 1 .23 given.

01:51 This is equal to 0 .4065...

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