Absolute Refractive Index Formula
The medium 1 is vacuum or air then the refractive index of medium 2 with respect to vacuum this is called absolute refractive index. This is denoted by n2.
The refractive index of medium nm is given by
nm = Speed of light in air/Speed of light in medium
nm = c/v ——- (3)
c = speed of light in air
v = speed of light in medium
This is also write as
n = Vair/Vmedium
Vair = Speed of light in air
Vmedium = Speed of light in medium
The refractive index of air is 1.0003 & refractive index of water is 1.33.
Numericals on Absolute refractive index Formula :
(1) Light travels with a velocity 1.8 × 108 m/s in a medium & enters into second medium its velocity becomes 0.95×108 m/s. What is the refractive index of the second medium with respect to 1st medium?
Given:
V1 = 1.8×108 m/s
V2 = 0.95×108 m/s
Refractive index = v1/v2 = 1.8×108/0.95×108 = 1.89
Refractive index have no unit because it is ratio of same quantity.
(2) The absolute refractive index of medium is 3. Velocity of light in vacuum is 3 × 108 m/s. What is velocity of light in medium?
Vair = 3×108 m/s
n = 3
Vmedium =?
n = Vair/Vmedium
3 = 3×108/Vmedium
Vmed = 3×108/3
Vmed = 1×108 m/s
Velocity of light in medium is 1×108 m/s
(3) Light passes from air medium into glass medium (n = 1.52) at an angle of incidence 65°. Calculate the angle of refraction?
Given:
n1 = 1.0
n2 = 1.52
n = c/v
θi = 65°
θr =?
n1 sinθi = n2 sinθr
(1.0) sin (65°)/1.52 = (1.52) sinθr/1.52
1.0×0.82/1.52 = sinθr
0.82/1.52 = sinθr
= 0.53 = sinθr
Θr = Sin-1 (0.53)
Θr = 32.0°
Angle of refraction is 32.0°
(4) A beam of light passes from air to another medium if angle of incidence is 68° and angle of refraction 50°. Find the refractive index of medium?
Given:
∠i = 68°
∠r = 50°
According to Snell’s law
Sin i/sin r = n
n = sin68/sin50
= 0.927/0.766
n = 1.21