A very narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 0.57 m thick flat block of crown glass and back to air ...

A narrow beam of light containing red (660 nm) and blue $(470 \mathrm{nm})$ wavelengths travels from air through a $1.00-\mathrm{cm}$ -thick flat piece of crown glass and back to air again. The beam strikes at a $30.0^{\circ}$ incident angle. (a) $\mathrm{At}$ what angles do the two colors emerge? (b) By what distance are the red and blue separated when they emerge?

Maybe more flight. That contends. Um, yeah. Red and blue light strikes the glass here, making an Anglo from 30 degrees with a normal here, 30 degrees. And then, uh, it disperses inside the glass so the red goes like this on, then it leaves the glass. Um, where's the blue disperses like this. And then it leaves the glass again. We had asked to find the emergent ingles, Um, for, uh, these two lights. So this is for this is for red. And this is for a blue. No way we can find an emergent angles using the relationship one that is a hey from air to glass, which we can write using Snell's law in a time, sign off the instant England incident in these people to reflect index off a glass times angle off refraction. Um, so let us do first for rig are red, then for red. We get the angle off. A fraction former did we get here is by substituting the values for her and the factory nix for red light, which is a a 1.512 for a loss. So we'll substitute this value here in energy and then substitute any. Which is one and incident angle is 30 degrees or by substituting those values we get here in the loft refraction. 19.31 16 days. Where is it? For a blue we get Anglo. Infraction is equal. Thio 1919.15 Hate the refractive index for the blue light. We're last use a 1.5 to 4 24 s o we will use the same relations will use their these refract tangles which will be the angle off incident when the light is going from a glassed over here. Sorry. Um so then we can find our emergent angle for red and blue by writing the relationship and off a glass times off signing glow for incident that we found, which is, uh, one for red. And that is equal to her front index off air times saying loaf emergent. So emergent tingle. So, like e inversiones, then substituting the value off a glass for red light, which is 1.12 We already wrote it. Then we can find a angle off emergent, and the angle off incident we have for red is 19.316 than a margin angle. We get hearings and 30 degrees. Similarly, we get emergent angle for a blue light again and 30 degrees. So this was about a Barbie were asked to find the distance between these two light rays when the march out off the glass so we can find the distance by writing the relationship for these triangles. So one form here to here and another one from here to here one for ah, they're so let me appreciate it is this is for from here to here for a blue and from here to here, the best is for grand light. Then we can write. We can call this for red light. We call this Opie Hopi to for a blue light. We call this Opie soapy one then, uh, Opie to convey mutinies. So I hope you two can. Burton is one times the tank off taking off from the 19.316 And this gives us the distance. Opie, which is a zero point three pies, five centimeter centimeter for will be one weekend. Right here. Here is ah which will give us for for a blue light which you will give us syrup on three 47474 And then we can find the difference which will give us the distance between these two light rays when they emerge out off the gas. The difference is, is it a 0.0? There are 31 said You went to three once in the end off the problem. Thank you.

In this problem we have given the wavelength of the red light, Linda R is equal to 670 nm linda B. That is where plenty of blue light is given edge 42 point so I'm just writing it here Linda BR 42.5 NM. The angle of incidents T T. Is equal to 30 degree. And the value of reflective index of the red light is given as 1.49 to 5. Now 3 to 2 is given a 0.131 radiant. So changing it in degree, I can like 0.131 multiplication 57.3 to 5 degree which is equal to zero point 075096 Now going forward I can write the value of sine theta two are which is equal to sine theta. I buy an ar which is equal to sign 30° by 1.49-5 Which is equal to 0.5 x 1.49-5 which is equal to 0.335. Now the value of theta two R. Is equal to sign in bus 0.335 which is equal to 19.573. Going forward here I can write the value of twitter to edge tita two ar minus treated to be which is equal to 19.573 -0.075096 which is equal to 19.4979 04. So the value of refractive index are blue light can be given by and B is equal to sign tita. I buy saying to to to be So just putting the value in this x person, I can write sign 30° by Sign 19.49704. Which one simplification I get the value of And B is equal to 1.4979 as our answer.

Applying snails law here so we can write this formula. This is the form laughs nail slaw. So teeter. One can be fine from here. So I am just putting the given data here. So these are the value that are given. So on calculating it, we get Tita. One is equal to this value now, Tita. Toe can also be calculated from snails law. So I am just writing the given data in the formula. So on solving this we get teeter toe is equal toe this value now as we know that, dear Tita is equal toe Tita one minus Tita toe. So I am just putting the value of theta one and Tita toe calculate Delta. So on subtracting this we get delta as three degree approx.

Hi Agreement. Here we have 25 angular respect. Yeah. Mm hmm. So and Far Capital Amble B. Same Universal capital Effective index and em into 40 degree. This angle is give it 40. So this will be also 40 according to snap's stock. Sine inverse. Aww. Yeah, Yeah. 1.533 into 40. So it is to be 18.19 degree and help for small amble. We signed and was off and into 40. That is sine inverse of 1.5 point seven and 2 40. So that is to be equal to 77 point point nine degrees. So angular spread you will get. Yeah, Mhm. That is 80.19 minus. That is to duty that so?