physics---(optics) VERY URGENT

refractive index = sin i/sin r

sin50/sin r = refractive index of medium X

Similarly,

sin r/sin 35 = refractive index of medium X

sin50/sin r =sin r/sin 35

(sin r)^2 = sin50xsin35

r=41.5

Figure (a) shows a light ray travelling from air into medium X. The angle of incidence is 50° and the angle of refraction is r.

Refractive index of air = 1.0003 (1.000)
Let the refractive index of medium X be N

We can have :

1 sin 50 = N sin r

Another light ray travelling from medium X to air is shown in Figure (b). The angle of incidence is 35 ° and the angle of refraction is also equal to r.

We can have :

N sin 35 = 1 sin r

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N sin 35 = 1 sin r
N = ( 1 sin r ) / ( sin 35 )

PUT N = ( 1 sin r ) / ( sin 35 ) INTO 1 sin 50 = N sin r

1 sin 50 = N sin r
1 sin 50 = [( 1 sin r ) / (sin 35)] sin r
sin 50 * sin 35 = ( sin r ) ^ 2
sin r = ( sin 50 * sin 35 ) ^ (1/2)
r = 41.5 ( corr. to 3 sig. fig. )

refractive index of air=1
Let the refractive indes of X = x
Form Figure a ,
we get, 1sin50=xsinr
i.e. x=sin50/sinr

Form Figure b,
we get, xsin35=1sinr
i.e. x=sinr/sin35

So we get sin50/sinr = sinr/sin35
sin50 x sin35 = sin^2 r
sin^2 r = 0.4394
sinr = 0.6629
r = 41.5度

sin50/sin r = refractive index of medium X

Similarly,

sin r/sin 35 = refractive index of medium X

sin50/sin r =sin r/sin 35

(sin r)^2 = sin50xsin35

r=41.5