What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?

Question

What is the required condition, if the light incident on one face of a prism, does not emerge from the other face? (A) n < cosec((A/2)) (B) n < sec ((A/2)) (C) n>sec A (D) n>cosec((A/2))

Tardigrade Admin · Accepted Answer

Consider the situation shown in figure.
Solution

Light rays

PQ

is incident on the face

A B

. It goes along

QR

and then along

RS

.
Here,

i =

angle of incidence at the face

A B

r_{1} =

angle of refraction through

A B

r_{2} =

angle of incidence at

A C

n =

refractive index of the material of the prims.
For the prism, we have

r_{1} + r_{2} = A

.....(i)
Now for light not to emerge from the face

A C,

r_{2} > C

Similarly for no emergence from the face

A B,

r_{1} > C

\Rightarrow r_{1} + r_{2} > 2 C

Here,

C

is critical angle.

\Rightarrow A > 2 C

[∵ r_{1} + r_{2} = A]

\Rightarrow \frac{A}{2} > C

\Rightarrow s in \frac{A}{2} > s in C

\Rightarrow s in \frac{A}{2} > \frac{1}{n}

\Rightarrow n > \frac{1}{s in \frac{A}{2}}

\Rightarrow n > cosec (\frac{A}{2})

Q. What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?

$n < cosec (\frac{A}{2})$

$n < sec (\frac{A}{2})$

$n > sec A$

$n > cosec (\frac{A}{2})$

Q. What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?

n<cosec(2A​)

n<sec(2A​)

n>secA

n>cosec(2A​)

$n < cosec (\frac{A}{2})$

$n < sec (\frac{A}{2})$

$n > sec A$

$n > cosec (\frac{A}{2})$