Question

A monochromatic light wave with wavelength $λ_1$ and frequency $v_1$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are 45° and 30° respectively, then the wavelength $λ_2$ and frequency $v_2$ of the refracted wave are :

• A. $λ_2 = 1/√2 λ_1, v_2 = v_1$
• B. $λ_2 = λ_1 , v_2 = 1/√2 v_1$
• C. $λ_2 = λ_1, v_2 = √2v_1$
• D. $λ_2 = √2λ_1 , v_2 = v_1$

Answer 1

Answer: (A)

$λ_2 = 1/√2 λ_1, v_2 = v_1$

Answer 2

1 × 𝑠𝑖𝑛45 = 𝜇𝑠𝑖𝑛30
⟹ 1 /√2 = 𝜇 × 1 2
⟹ 𝜇 = √2− − − −(𝑖)
Now, 𝜇_1 /𝜇_2 = 𝑉_2 𝑉_1 = 𝜆_2/ 𝜆_1 − −− − − (𝑖𝑖)
Using eq (i) and (ii), 𝜆2 = 1 /√2 𝜆_1
And 𝑉_2 = 1 /√2 𝑉_1
Now, for relation between frequencies,
Frequency, 𝑣 = 𝑉/𝜆
Or 𝑣1/𝑣2 = 𝑉_1/𝑉_2 × 𝜆_2/ 𝜆_1 = 1
𝑣_1 = 𝑣_2