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 = 370 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 (b) ma = 4 and (c) ma = 5?

Question

Physics

Adalyn Sims

12 October, 15:41

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 = 370 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 (b) ma = 4 and (c) ma = 5?

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Luca Benton · Answer 1

First minimum of λa will be formed at 1 x λa D/d distance from the centre where D is distance of screen and d is width of slit.

As per given statement

λa D/d = 2 x λb D/d

λa = 2 x λb

= 2 x 370 nm

= 740 nm

Let ma th order of λa component coincides with mb the order of λb component

ma λa D/d = mb λb D/d

ma / mb = λb / λa

ma / mb = 1 / 2

mb = 2 ma

if ma = 4

mb = 8

if ma = 5

mb = 10