Question

when a ray of light travelling from vacuum to a medium of refractive index u the angle of incidence is twice the angle of refraction.the incident angle theta is​

Answer 1

Explanation:

Let i be the incident angle and r be the refracted angle

given, 1=2r⇒r=

2

i

the refractive index of vacuum is 1 and that of another medium is n

from snell's law,

1sini=nsinr

⇒sini=nsin(

2

i

)

2sin(

2

i

)cos(

2

i

)=nsin(

2

i

)

⇒sin(

2

i

)[2cos(

2

i

)−n]=0

sin(

2

i

)=0=sinπ⇒i=2π

[2cos(

2

i

)−n]=0⇒i=2cos

−1

(

2

n

)

therefore the value of incident angle =2cos

−1

(

2

n

)