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A beam of light passes from air into a substance X. If the angle of incidence be `72^(@)` and the angle of refraction be `40^(@)`, calculate the refractive index of substance X. (Given: `sin72^(@)=0.951` and `sin40^(@)=0.642)`

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We know that:
Refractive index `= ("Sine of angle of incidence")/("Sine of angle of refraction")`
or `n=("sin I")/("sin r")`
Here, Angle of incidence, `i=72^(@)`
And, Angle of refraction, r=`40^(@)`
So, `n=(sin72^(@))/(sin 40^(@))`
We are given that sin `72^(2)=0.951` and sin `40^(@)=0.642`. So putting these values of sin `72^(@)` and sin `40^(@)` in the above relation, we get:
`n=(0.951)/(0.642)`
or n=1.48
Thus, the refractive index of substance X is `1.48`.
So far we have denoted the refractive index of a substance just by the letter n. It its full form, the refractive index n has, however, two subscripts (lower words or letters) which show the two substances or media between which has light travels. For example, the refractive index for light going from air into glass is written as `._("air")n_("glass")` ( or `._(a)n_(g)` where a = air and g=glass). We will discuss this in more detail after a while.

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