State the law of refraction of light that defines the refractive index of a medium with respect to the other. Express it mathematically. How is the refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B? State the name of this constant when one medium is vacuum or air. The refractive indices of glass and water with respect to vacuum are 3/2and 4/3 respectively. If the speed of light in glass is 2x108 m/s, find the speed of light in (i) vacuum, (ii) water.
Answers
Explanation:
It establishes a relation between angle of incidence and angle of refraction. It can be expressed mathematically as follows : n nis constant and is known as refractive index. When one medium is vacuum or air and light is going to another medium, then the constant is known as absolute refractive index.
The second law of refraction is also known as Snell's law of refraction and it states that the ratio of Sine of the angle of incidence to the sine of refraction is constant for a given pair of media. It establishes a relation between angle of incidence and angle of refraction.
It can be expressed mathematically as follows :
n nis constant and is known as refractive index.
The refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B can be written as follows:
Where, Vp is the speed of light in medium 'B' and VA is the speed of light in medium 'A'
B'A is the refractive index of medium 'A' with respect to medium 'B'
When one medium is vacuum or air and light is going to another medium, then the constant is known as absolute refractive index.
Given: Refractive index of glass,
Vw-4/3
speed of light in glass, ug =2x108 m/s
Applying the formula:
Putting the above values
Therefore, velocity of light in vacuum is 3 x 108m/s
Now, for calculating the velocity of light in air
Applying the formula:
Therefore, velocity of light in air is 2.25x108 m/s
Answer:
Snell's law of refraction states that the ratio of sine of angle of incidence in the first medium to the sine of angle of refraction in the second medium is a constant and is termed as the refractive index of the second medium with respect to the first medium,
1
2
sin
sin
i
n
r
where i and r are the angle which the incident and refracted rays respectively make with the normal.
The constant 1
2 n is called the refractive index of the second medium (2) relative to the first medium (1).
Relation between refractive index of any medium 'A' with respect to a medium 'B' and the speed of propagation of light in two media A and B:
B
A n =
Speed of light in medium B
Speed of light in medium A