The absolute refractive indices of glass and water is 4/3 and 3/2,respectively. If the speed of light in glass is 2x108m/s,calculate the speed of light in a. Vacuum b. Water?

Question

Answer

Given,

*Refractive indice of Glass = 4/3 = 1.33.

* Refractive indice of Water = 3/2 = 1.5.

Speed of light in glass = 2×108m/s.

a) Speed of light in vaccum = 3×108.

n = Velocity of light in vaccum/Velocity of light in specific medium.

1.3 = 3×108/ Vg ( Vg refers to Velocity of glass).

Vg = 3×108/1.3

= 30/1.3
Vg = 2.3×108m/s.

b) Speed of light in water = ?

n = Speed of light in Vaccum/Speed of light in specific medium.

1.5 = 3×108/Vw (Vw refers to Velocity of water).

Vw = 3×108/1.5

= 30/1.5

Vw = 2×108m/s.

Therefore, the speed of light in Vaccum and Water is 2.3×108m/s and 2×108m/s.

(Note:- 108 is 10 to the power of 8)

Answer

Solution : Refractive Index of glass glass = speed of light in vacuum /speed of light in glass

4/3 = speed of light in vacuum/2 × 10 power 8

speed of light in vacuum= 2.6 × 10 power 8 m/s

But ideally the speed of light in vacuum is 3 × 10 power 8 m/s

Refrective index of water = 2.6 × 10 power 8 /speed of light in water

= 1.73 × 10 power 8 m/s

Answer

Calculation of Speed of Light in Vacuum and Water

Given:

Absolute refractive index of glass (μ_g) = 4/3

Absolute refractive index of water (μ_w) = 3/2

Speed of light in glass (v_g) = 2 x 10⁸ m/s

To Find:

Speed of light in vacuum (v₀)

Speed of light in water (v_w)

Solution:

Step 1: Calculate the relative refractive indices of glass and water.

Relative refractive index of glass w.r.t air = μ_g/air = μ_g/μ_air = 4/3

Relative refractive index of water w.r.t air = μ_w/air = μ_w/μ_air = 3/2

Step 2: Calculate the speed of light in vacuum.

Speed of light in vacuum (v₀) = v_g/μ_g/air = (2 x 10⁸ m/s)/(4/3) = 1.5 x 10⁸ m/s

Step 3: Calculate the speed of light in water.

v_g/v_w = μ_g/μ_w

v_w = v_g/μ_g x μ_w

v_w = (2 x 10⁸ m/s)/(4/3) x (3/2) = 1.5 x 10⁸ m/s

Answer:

Speed of light in vacuum (v₀) = 1.5 x 10⁸ m/s

Speed of light in water (v_w) = 1.5 x 10⁸ m/s

Explanation:

The speed of light in a medium is related to its refractive index. The refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium. In this question, the absolute refractive indices of glass and water are given. We first need to calculate the relative refractive indices of these mediums w.r.t air. Using these values, we can then calculate the speed of light in vacuum using the formula v₀ = v_g/μ_g/air. Similarly, we can calculate the speed of light in water using the formula v_w

Answer

Answer:

Explanation:

Solution :-

Refractive index of a medium = Speed of light in air/Speed of light in medium

3/2 = Speed of light in air/2 *10⁸ m/s

Speed of light in air = 3 * 10⁸ m/s

1. In Vacuum -

Speed of the light in vacuum = 2 * 10⁸ m/s/3/2

Speed of the light in vacuum = 3 *10⁸ m/s

Hence, the speed of light in vacuum is 3 *10⁸ m/s.

2. In Water -

Speed of the light in water = 3 *10⁸ m/s/4/3

Speed of the light in water = 2.25 * 10⁸ m/s

Hence, the speed of light in water is 2.25 * 10⁸ m/s.

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