0:00
Hello everyone.
00:01
The question here is that there is a prism which is made of a certain type of glass and it is equilateral in nature.
00:09
So all of the angles are 60 degrees and now white light is being incident on this prism from one side so it is a white light and the prism has different refractive index index index indexes for red and violet each and for reflecting windows for red is 1 .656 and fractive index is 1 .674 the values are given here and now we have to find in part a the angle of refraction of red is on the when it is emerging into the air so we have to find this angle this angle this angle this angle be a so we have to find that and the angle a in part a so we'll first proceed in the case of a as this is this is a the light curve going and it is this is the light going and then it splits into red color and then it emerges out so we know that this angle is 60 degree the angle of incidence on the prism is 60 degree and this angle is 260 degree because it is equilateral triangle so we know that we know the refractive index for red which is 1 .656 so using snell's law we can calculate this angle which is this i let's give it an i so we know that so we'll write the stens law for the processes having on this surface so we know that the slens law is muon sine theta 1 equals to mu 2 sine theta 2 so mu 1 first is air and is 1 and sine theta is sine 60 degree and mu 2 in the glass of red mu red is 1 .656 multiplied by sine theta 2.
02:19
You know the value of 60 degree is root 3 by 2 and multiplied by 1 by 1 .656 is equal to sine theta 2 so from here we'll get the value of theta 2 so the theta 2 here is i so so, sine i equals to root 3 by 2 multiplied by 1 by 1 .66.
02:49
So if we apply sine inverse formula, then the value of i would be 31 .15 degree.
02:57
It's actually 31 .5 degree.
03:01
So we know this value i and now we also know this value this value this must be 90 minus i.
03:09
90 minus i so so this let us say this as so now if it is 90 minus i then we can know the value of this angle let us give this angle as x so angle x would be 180 degree minus 60 degree minus i where it is in bracket so x would be 30 degree plus i so it is a bracket so x would be 30 degree plus i so it is 61 .5 degree.
03:44
So we know the value of x.
03:46
Now we can calculate the incident the incident angle which is which is the ray of red light is making at the other surface.
03:56
So let us this incident angle be as y.
03:59
So y would be 90 degree minus x so value of x is 61 .5 degree.
04:09
So y here is we can easily see that y is 28 .5 degree so now we know the value of y so now we can calculate again use snell's law and we can calculate the angle of emerging emergence which is a so now we'll again use snell's law snell's law over this this surface so first angle of first we'll write the the refractive index of red which is 1 .65 and multiplied by the sign of this angle which is sine y is equal to and the reflective index in air is 1 is equal to sine a so 1 .65 into sine y is 28 28 .5 degree 28 .5 degree equal to sine a the value of sign 28 degree is 0 .477 so if we put it here 65 into 0 .477 equal to sine a now we shall calculate the value of a through sine inverse so the value of a would be if we calculate it carefully it would be 52 .09 degree so the answer of first part is 52 .09 degree which is the angle of refraction at the emergence of a in the air now in part b we have to find the same angle of refraction at the emergence at this emergence point and but for the violet light so we'll proceed by the same process first we'll draw the figure and then this is the violet light the incident angle is 60 degree we all know this is also 60 degree but now this i will differ because the interactive index of violet is differing.
06:22
The active index of violet is 1 .674...