Question

Parallel beam containing light of a = 400 nm and 500 nm is incident on a prism as shown. TH
refractive index n of the prism is given by the relation na = 1.20+
0.8 x 10-14
2²
A
B В
С
Given sin 0 =0.8. Then which of the following statement is correct?
1) Light of 2 = 400 nm undergoes total internal reflection
2) Light of 2 = 500 nm undergoes total internal reflection
3) Neither of the two wavelengths undergo total internal reflection
4) Both the wavelengths undergo total internal reflection​

Answer 1

Explanation:

first option is correct

Answer 2

option (1) is the correct answer

Given:

λ = 400 and 500

μ(λ) = 1.20 + 0.8 x10^-14/ λ²

To find:

Which of the following statements is correct?

(1) Light of λ = 400 nm undergoes total internal reflection

(2) Light of λ = 500 nm undergoes total internal reflection

(3)  Neither of the two wavelengths undergo total internal reflection

(4)  Both wavelengths undergo total internal reflection

Solution:

we already know that,

Θ = r1 + r2

where r1 = 0 and r2 = Θ

now, the ray will undergo total internal reflection from the second refracting surface,

if Θ = r2 > sin^-1(1/μ)

==>  sinΘ ≥ 1/μ

==>  μ > 1/sinΘ

==>  1/sinΘ = 1/0.8 = 1.25

now,

μ(400nm) = 1.2 + 0.8* $10^-14$/$(400 * 10^-9)^2$ = 1.25

μ(500nm)<1.25

hence, only 400 nm will show total internal reflection.