Question

1. The speed of light in a medium was (2*10^8) m/sec.
What is the refractive index of the medium?

2. Light enters from water to a glass plate. The refractive index of the glass is 9/8 with respect to water. The speed of light in vacuum is (3*10^8) m/sec. The speed of light in the glass plate is (2*10^8) m/sec. Find:
a) The refractive index of the glass plate
b) The refractive index of water

Answer 1

Given :

▪ Speed of light in medium = 2×10^8 mps

To Find :

▪ Refractive index of the medium.

Solution - 1)

→ Refractive index of a medium is defined as the ratio of speed of light in the vaccum to the speed of light in the medium.

→ It is an unitless as well as dimensionless quantity.

Mathematically,

☞ n = C / V

• n denotes refractive index
• C denotes speed of light in the vaccum
• V denotes apeed of light in the medium

▪ We know that, C = 3×10^8 mps

✒ n = (3×10^8) ÷ (2×10^8)

✒ n = 3/2

✒ n = 1.5

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Given :

▪ Refractive index of glass wrt water = 9/8

▪ Speed of light in glass = 2×10^8 mps

▪ Speed of light in vaccum = 3×10^8mps

To Find :

▪ Refractive index of glass plate (n_g)

▪ Refractive index of water (n_w)

Solution - 2)

✴ Refractive index of glass :

✒ n_g = C / V_g

✒ n_g = (3×10^8)÷(2×10^8)

✒ n_g = 3/2

✒ n_g = 1.5

✴ Refractive index of water :

✏ Refractive index of glass wrt water is given by

☞ n_(gw) = n_g / n_w

☞ 9/8 = 1.5/n_w

☞ n_w = (1.5×8)/9

☞ n_w = 4/3

☞ n_w = 1.33

Answer 2

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$\huge\tt{GIVEN:}$

• The speed of light in a medium was (2*10^8) m/sec

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$\huge\tt{TO~FIND:}$

• The refractive index of the medium

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$\huge\tt{SOLUTION:}$

Reflective Index - It is defined as the ratio of speed of light in the vaccum to the the speed of light in a medium.

So, Mathematically,

↪n = C / V

We know that,

↪C = 3 × 10^8

↪n = (3×10^8) ÷ (2×10^8)

↪n = 3/2

↪n = 1.5

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$\huge\tt{GIVEN:}$

• Light enters from water to a glass plate.
• The refractive index of the glass is 9/8 with respect to water.
• The speed of light in vacuum is (3*10^8) m/sec.
• The speed of light in the glass plate is (2*10^8) m/sec.

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$\huge\tt{TO~FIND:}$

• The refractive index of the glass plate
• The refractive index of water

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$\huge\tt{SOLUTION:}$

✡ Reflective Index of glass ✡

↪n_g = C/V_g

↪n_g = (3×10^8) / (2×10^8)

↪n_g = 3/2 or 1.5

✡ Reflective Index of Water ✡

↪n_(gw) = n_g / n_w

↪9/8 = 1.5/n_w

↪n_w = (1.5×8)/9

↪n_w = 4/3

↪n_w = 1.33

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