Question

Light enters at an angle of incidence in a
transparent rod of refractive index u. For
what value of the refractive index of the
material of the rod the light once entered
into it will not leave it through its lateral
face whatsoever be the value of angle of
incidence?​

Answer 1

Answer:

Let angle of incidence be B

i

& angle of refraction be B

r

We went be light to not escape from the lateral side & we know that critical angle is the angle at which refracted ray grages the surface at 90

o

The light has highest chance of escaping from lateral side if θ

i

=90

o

(a) θ

i

=90

o

:1.sinθ

i

=n,sinθ

r

|snell law

⇒sinθ

r

=

n

1

....(i)

If his ray grages the surface on lateral side the for all other θ

i

(θ

i

<90

o

) there will be total internal reflection

at lateral surface : n.sin(90−θ

r

)=1.sin90

o

⇒n.cosθ

r

=1 from (i)

⇒n=

n

n

2

−1

=1

⇒n

2

=2

⇒n=

2

For any n greater than this limiting we there will be total internal reflection for any angle of incidence.