How Is Wavelength Calculated in Single Slit Diffraction?

[moatasim23]

Homework Statement

What is the wavelength of the light whose first diffraction max (not counting the central max) falls at 15°,thus coinciding with the first min for red light?Width of slit=2510 nm."
It is an example problem from Halliday Resnik Krane..In which the they use the principle that max occurs half way b/w two min.and used the angles for two minimas as 10°and 20°.How can u arbitrarily choose two angles?IN this way can't u use 5° and 25°?But then wavelength would be wrong..What is the significance of these two angles :10° and 20°?



This wasnt a homework question.It was a solved exercise In the Book Physics by Halliday,Resnick,Krane.How can I show my attempt when it is already solved in the book?I just couldn't comprehend the solution fully.So I asked the question..BTW its answer is wavelength violet =430..
and we use the formula λ'=1/2(2510)(sin20°)=430nm

 

[_coyote_]

.Homework Equations λ = 1/2(d)(sinθ)The Attempt at a Solution The solution to the problem is that the wavelength of the light whose first diffraction max falls at 15°, thus coinciding with the first min for red light, is 430 nm. This can be calculated using the equation λ = 1/2(d)(sinθ), where d is the width of the slit (in this case, 2510 nm) and θ is the angle at which the diffraction max occurs (in this case, 15°). Substituting these values into the equation yields λ = 1/2(2510)(sin15°) = 430 nm.