CS602 ASSIGNMENT NO 2 SOLUTION 2023 || cs602 assignment no 2 solution fall 2023 || download link || comtech for students

The angle of refraction can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two materials.

For this problem, we can use Snell's law to find the angle of refraction:

sin(θr) = (n1/n2) * sin(θi)

where

θi = angle of incidence in glass (35°) n1 = refractive index of glass (1.62) n2 = refractive index of water (1.22)

Plugging in the values:

sin(θr) = (1.62/1.22) * sin(35)

To find the equation of the normal to a plane, we can use the coordinates of three non-collinear points that lie on the plane. The normal is a vector that is perpendicular to the plane, and it can be found by taking the cross product of two vectors that lie on the plane.

Given the points P1(8.0,7.0,3.0), P2(2.0,2.0,2.0), and P3(6.0,6.0,4.0), we can first find the two vectors that lie on the plane by subtracting the coordinates of P1 from those of P2 and P3:

P2P1 = <2.0-8.0,2.0-7.0,2.0-3.0> = <-6.0,-5.0,-1.0> P3P1 = <6.0-8.0,6.0-7.0,4.0-3.0> = <-2.0,-1.0,1.0>

The normal can be found by taking the cross product of these vectors:

N = P2P1 x P3P1 = <-5.0 + 2.0, 6.0 + 2.0, -1.0 - 2.0> = <-3.0,8.0,-3.0>

Now we can find the equation of the plane by finding the dot product of the normal and any point that lies on the plane. Let's use P1

<a,b,c> . <8.0,7.0,3.0> = a8.0 + b7.0 + c3.0 = -38.0 + 87.0 -33.0 = -24.0 + 56.0 - 9.0 = 23

So, the equation of the plane is:

ax + by + cz = 23

Where the normal to the plane P is <-3.0,8.0,-3.0>

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