1.

State the law of refraction of light that defines the refractive index of a medium with respect to the other. Express it mathematically. How is refractive index of any medium A with respect to a medium B relate to the speed of propagation of light in two media A and B ? State the name of this constant when one medium is vacuum or air ? The refractive indices of glass and water with respect to vacuum are (3)/(2) and (4)/(3) respectively. If the speed of light in glass is 2 xx 10^(8) ms^(-1), find the speed of light in (i) vacuum, (ii) water.

Answer»

Solution :Snell.s law defines the refractive index of a medium with respect to the other. For its statement and mathematical expression, see Point Number 21 under the heading "Chapter At A Glance". Refractive index of a medium A with respect to a medium B `(n_(AB))`
`= ("Speed of light in medium B" (v_(B)))/("Speed of light in medium A" (v_(A)))`
If ONE medium is AIR or vacuum then this constant is known as the (absolute) refractive index of the other medium. Thus,
Refractive index of a medium (n) `= ("Speed of light in vacuum/air (c)")/("Speed of light in the medium (v)")`
As per question `n_(g) = (3)/(2) and n_(W) = 2 xx 10^(8) ms^(-1) and v_(g) = 2 xx 10^(8) ms^(-1)`
(i) `because n_(g) = (c)/(v_(g))` hence speed of light in vacuum `= n_(g).v_(g) = (3)/(2) xx 2 xx 10^(8) = 3 xx 10^(8) ms^(-1)`
(II) Speed of light in water `v_(w) = (c)/(n_(w)) = (3 xx 10^(8))/(4//3) = 2.25 xx 10^(8) ms^(-1)`


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