Question

Therefractive index of diamondis 2.4 andrefractive
index of diamond with respect to glass is 1.6. The
speed of light in glass is lassuming speed of light in
air is 3 x 108 ms -​

Answer 1

Given :

▪ Refractive index of diamond = 2.4

▪ Refractive index of diamond wrt glass = 1.6

▪ Speed of light = 3×10$^8$m/s

To Find :

➾ Speed of light in glass.

Concept :

➛ Refractive index of a medium is defined as the ratio of speed of light in vacuum to the speed of light in medium.

Mathematically,

✭ n = c / v

where,

◕ n denotes refractive index

◕ c denotes speed of light in vaccum

◕ v denotes speed of light in medium

➛ Refractive index of medium 1 wrt medium 2 is given by

✭ n(12) = n(1) / n(2)

Calculation :

✴ Refractive index of glass :

➠ n(dg) = n(d) / n(g)

➠ 1.6 = 2.4 / n(g)

➠ n(g) = 2.4/1.6

➠ n(g) = 3/2

✴ Speed of light in glass :

⇒ n(g) = c / v(g)

⇒ 3/2 = 3×10$^8$/v(g)

⇒ v(g) = 2×10$^8$ m/s

Answer 2

Given :-

• Refractive index of diamond = 2.4
• Refractive index of diamond with respect to glass = 1.6.
• Speed of light = 3 × 10^8 m/s

To find :-

• Speed of light in glass = ?

Solution :-

★ Refractive index of glass :-

→ n(dg) = n(d)/n(g)

→ 1.6 = 2.4/n(g)

→ n(g) = 2.4/1.6

→ n(g) = 3/2

★ Speed of light in glass :-

→ n(g) = c/v(g)

→ 3/2 = 3 × 10^8/ v(g)

→ v(g) = 2 × 10^8 m/s