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The prism in Figure $P 22.32$ is made of glass with an index of refraction of 1.64 for blue light and 1.60 for red light. Find (a) $\delta_{R},$ the angle of deviation for red light, and (b) $\delta_{B},$ the angle of deviation for blue light, if white light is incident on the prism at an angle of $30.0^{\circ} .$

a. $18.92^{\circ}$

b. $20.23^{\circ}$

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University of Michigan - Ann Arbor

Numerade Educator

University of Washington

University of Winnipeg

we're told the angle of incidence of light fatal one is 30 degrees on a prism where the index of refraction for blue light, which I call into CID be is 1.6 floor and the index of refraction for red light in Tucson bars 1.60 index refraction for air is 1.0. So into two in one ratio is equal to sign 1/2 of fatal one plus this, uh, delta value. So the delta value here is the, um, angle of deviation, and that's what we're trying to find. So it's fatal. Plus delta value divided by sign 1/2 of index of incident Earth. The angle of incident, which is stable one. So we can use this to find that, uh, that angle of DD deviation delta. So for part A here grass to do this for the case of red light. So solving for Delta and we're gonna call this Delta are for Red Light. This is going to be equal to two. We're just solving for that. Dealt are times the inverse side of the ratio of into our two in one times signed 1/2 data one and then minus data one. So plugging those values in this expression, we find that this is equal to 18.92 degrees. You can go ahead and box that in. That's your solution. For part a part B. We're gonna do the exact same thing except for in this case, we're gonna do it for the blue light. So then this is going to be Delta Bi for Blue. This is going to be equal to two. I'm signed in the minus one of the ratio of index of refraction for blue. We called that into B thio Any index of refraction for air in one times sign 1/2 of data one and then all that is minus data one. Plugging those values into this expression we find dealt to B is equal to 20 point to three degrees, which could be boxed in as our solution for part B