A prism is in the shape of an equilateral triangle an...

A prism is in the shape of an equilateral triangle. An incoming beam of white light strikes the prism at 78 degrees with respect to the normal, as shown in Figure P21.62. The refractive indices for far red (700 nm) and far violet (400 nm) are 1.62 and 1.65, respectively. Find the angles at which the two colors emerge on the other side of the prism, and compute the angular spread of the light.

Transcript

00:02 Hi, here in this given problem first of all we draw an equilateral glass prism a little bigger one to show the details, close details.

00:16 This is the prism, equilateral prism so this angle will be 60 degree.

00:22 Then to incident a light, a beam of light over it, first of all we draw a normal over the surface.

00:31 Refracting surface of the prison this is the normal then with this normal a ray of light is incident and here that is this ray of light is making an angle of 78 degree with the normal this is 78 degree now it will be refracted into the material of the prism such that the violet suppose we are supposing it to be the mixture of two colors.

01:10 One of the color is violet.

01:13 Suppose we represent it by the blue only.

01:19 Here it goes like this and another that is red.

01:26 It will be going like this.

01:28 Suppose.

01:29 Then they will come out into the air again so we'll have to draw two normals now this is the normal for the refraction of violet light and here this is the normal for the refraction of the red colored light and then finally these rays will emerge into the air again like this here we have to find the final angles of emergent of these rays this will be i b for the blue sorry violet i and here this will be i r for red but to find them we should have angles of refraction also means these values we should have so you will find them later on and these angles will serve as the angles of incident sorry i have marked it wrong these are angles of refraction r r and r v or we can say emergence again i'm making a change here these will be the angles of emergence so these will be marked as e r and e v okay finally and here these will be the angles of incidence for these two different colors.

03:14 So this is i r and here this will be i.

03:19 V.

03:20 And then these will be the angles of refraction.

03:24 This bigger one that is rr and this smaller one, smaller one that is rv...

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