Question

1)The speed of light in a certain substance is 77.28-% of its value in crown glass. What is the index of refraction of that substance?

2)The speed of light in a certain substance is 81.7-% of its value in water. What is the index of refraction of that substance?

3)What is the speed of light in (km/s) in a material that has an index of refraction of 3.59?

Answer 1

1) we know, refractive index of a medium(n) = velocity of light in vacuum(c) velocity of light in the medium (v)

now refractive index of crown glass = 1.52 (approx),

so speed of light in crown glass is, (v_c) = C 1.52 =1.97 10⁸ m/s

So, speed of light in the substance is = (77.28 100) 1.97 10⁸ = 1.5210⁸ m/s

2) From definition of refractive index we can write,

where n_s= refractive index in substance,  n_w= refractive index in water= 1.33

v_s= velocity of light in substance, v_w= velocity of light in water.

Now, given

  

so ,

So,  

3) Here refractive index of the medium is, n =3.59,

So speed of light in the medium is,