Question

A single slit is illuminated by light of wavelengths λa and λb, chosen so that the first diffraction minimum of the λa component coincides with the second minimum of the λb component. (a) If λb = 350 nm, what is λa? For what order number mb (if any) does a minimum of the λb component coincide with the minimum of the λa component in the order number

Answer 1

λ_A = 700 nm , m_B = m_a 2

Step-by-step explanation:

The expression that describes the diffraction phenomenon is

a sin θ = m λ

where a is the width of the slit, lam the wavelength and m an integer that writes the order of diffraction

a) They tell us that now lal_ A m = 1

a sin θ = λ_A

coincidentally_be m = 2

a sin θ = m λ_b

as the two match we can match

λ _A = 2 λ _B

λ_A = 2 350 nm

λ_A = 700 nm

b)

For lam_B

a sin λ_A = m_B λ_B

For lam_A

a sin θ_A = m_ λ_ A

to match they must have the same angle, so we can equal

m_B λ_B = m_A λ_A

m_B = m_A λ_A / λ_B

m_b = m_a 700/350

m_B = m_a 2