# The absolute refractive indices of glass and water are 4/3 and 3/2, respectively. If the speed of light in glass is 2 × 10^8 m/s, calculate the speed of light in - Science

The absolute refractive indices of glass and water are 4/3 and 3/2, respectively. If the speed of light in glass is 2 × 108 m/s, calculate the speed of light in

(a) vacuum (b) water

#### Solution

Refractive index of glass, ηg = 4/3

thereforeeta_g="Speed of light in vacuum"/"Speed of light in glass"

4/3="Speed of light in vacuum"/(2xx10^8)

"Speed of light in vacuum "=(4xx2xx10^8)/3=2.6xx10^8"m/s"

"Refractive index of water,"eta_w=3/2

eta_w="Speed of light in vacuum"/"Speed of light in water"

3/2=(2.6xx10^8)/"Speed of light in water"

"Speed of light in water" = 1.73 xx 10^8 "m/s"

Because the information provided is wrong, ideally the speed of light in vacuum is 3 × 10⁸ m/s and the speed of light in water is 2.25 × 10⁸ m/s.

The correct solution is

"Refractive index of glass,"eta_g=3/2

"Refractive index of water,"eta_w=4/3

"Refractive index of glass,"eta_g="Speed of light in vacuum"/"Speed of light in glass"

3/2="Speed of light in vacuum"/(2xx10^8)

"Speed of light in vacuum "=(3xx2xx10^8)/2=3xx10^8"m/s"

"Refractive index of water, "eta_w=4/3

eta_w="Speed of light in vacuum"/"Speed of light in water"

4/3=(3xx10^8)/"Speed of light in water"

"Speed of light in water "=(3xx3xx10^8)/4

"Speed of light in water "=2.25xx10^8"m/s"

Concept: Refractive Index
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2014-2015 (March) All India Set 1
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