Question

Calculate critical angle whose refractive index is 1
/2​

Answer 1

The critical angle is the angle of incidence where the angle of refraction 90

0

. The light must travel from an optically more dense medium to an optically less dense medium.

Prof:−

Instead of always having to measure the critical angles of different materials, it is possible to calculate the critical angle at the surface between two media using snell's Law. To recap, sneel's Law states:

n

1

sinθ

1

=n

2

sinθ

2

Where n

1

is the refractive index of material 1, n

2

is the refractive index of material 2, θ

1

is the angle of incidence and θ

2

is the angle of refraction . For total internal reflection we know that the angle of incidence is the critical angle, so,

θ

1

=θ

c

.

However, we also know that the angle of refraction at the critical angle is 90

0

. So we have

θ

2

=90

0

WE can then write snell's Law as:

n

1

sinθ

c

=n

2

sin90

0

Solving for θ

c

gives:

n

1

sinθ

c

=n

2

sin90

0

sinθ

c

=

n

1

n

2

(1)

θ

c

=sin

−1

(

n

1

n

2

)

Hence, we proved.