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

The Correct Option is A

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