Question

find refractive index of water with respect to glass if the speed of light in water and glass is 2.25×10^8 m/s and 2×10^8 m/s respectively​

Answer 1

Answer:

2.25(10⁸)/2(10⁸)

2.25/2

1.125

is the refractive index

Answer 2

Given :

• speed of light in water = 2.25 × 10⁸ ms⁻¹
• speed of light in glass = 2 × 10⁸ ms⁻¹

To find :

• Refractive index of water with respect to glass

Knowledge required :

The refractive index of medium 2 with respect to medium 1 is equal to the ratio of speed of light in medium 1 to the speed of light in medium 2.

(➠ Refractive index is generally denoted by R.I. or n )

$\gray{\bigstar}\boxed{\sf{_{1}n_{2} = \dfrac{v_1}{v_2}}}$

( where ₁n₂ is refractive index of medium 2 with respect to medium 1  ; v₁ is the speed of light in medium 1  and v₂ is the speed of light in medium 2 )

Solution :

Using the formula

$\sf{_{1}n_{2} = \dfrac{v_1}{v_2} }$

Refractive index of water with respect to glass will be

$\implies\sf{ = \dfrac{speed \: of \: light \: in \: glass}{speed \: of \: light\: in \: water} } \\ \\ \implies \sf{ \dfrac{2 \times {10}^{8} }{2.25 \times {10}^{8} }=\dfrac{2}{2.25} } \\ \\ \implies \large{\red{ \sf{0.89}}}$

Hence, refractive index of water with respect to glass is 0.89  (approximately).

Know more :

● Refractive index of a medium with respect to air ( or vacuum) is considered to be it's absolute refractive index.

● The refractive index for light going from medium 1 to medium 2 is equal to the reciprocal of the refractive index for light going from medium 2 to medium 1.

●  Refractive index of medium 1 with respect to medium 2 can also be given as the ratio of absolute refractive index of medium 1 to the absolute refractive index of medium 2.