Question

1)The index of refraction of light in diamond is 2.448. What is the speed of light in diamond? Answer in units of m/s.

2)The angle of incidence and the angle of refraction for light going from air into a material with a higher index of refraction are 63.4 ◦ and 45.0 ◦ , respectively. What is the index of refraction of this material?

Answer 1

1)The index of refraction of light in diamond is n = 2.448.

speed of light inside of diamond v =c/ n = 3*10^8/2.448. =1.2254902*10^8 m/s

2)The angle of incidence and the angle of refraction

apply snells law at the incident surface

n1*sin1 = n2 *sin2

here n1 = 1 for air  

1 * sin ( 63.4) = n2 *sin45

solve for n2

n2 = sin( 63.4) / sin45 = 1.2645  

refraction of this material​ = ​1.2645  

let me know in a comment if there is any problem or doubts