Question

The figure below shows a layer of oil that is floating on water in a glass container. Refractive index of oil = 1.47; Refractive index of water = 1.33; Refractive index of the glass = 1.47. The value of the angle of refraction in glass is:

Answer 1

Answer:

Let the incidence angle at water-oil interface be i, and the refraction angle be r, which also acts as the incidence angle at oil-air interface.

Then, at the water-oil interface by Snell's law:

sini

sinr

=

n

o

n

w

⇒sinr=

n

o

n

w

sini

Again, for Total internal reflection at oil-air interface, by Snell's law:

sinr

sin90

∘

=

1

n

o

(since, n

air

≈1)

⇒sinr=

n

o

1

⇒

n

o

n

w

sini=

n

o

1

⇒sini=

n

w

1

∴i=sin

−1

(

n

w

1

)=C

Thus, the critical angle C for total internal reflection is independent of n

o

.