Light from a lamp, which emits light a several discreet different wavelengths, i

Question

Light from a lamp, which emits light a several discreet different wavelengths, illuminates an 800 line/mm diffraction grating. A screen is placed 50.0 cm behind the grating where the light is observed. Light of wavelength 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum, (a) What is the wavelength of the first-order bright fringe that is 37.80 cm from the central maximum? (b) If the screen is very long, what is the maximum number of bright fringes for the light of wavelength 501.5 nm?

Explanation / Answer

In interfreence or diffraction pattern

the needed equation is Y = mLR/d---------------1

and d sin theta = mL--------------------2

where L = wavelgnth

m = order = 1,2,3,4, ......... for brigth bands

m = 1.5, 2.5, 3.5, 4.5, ......for dark bands

R is the distance from slit to screen

Y = disatnce from central spot to nth order fringe or fringe width

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so here we apply L = Yd/mR

apply L2/L1 = Y2/Y1

L2 = 37.8*501.5nm/21.9

L2 = 865.60 nm

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d sin theta = mL

m = (1/800mm) sin 90/856.6nm

m = 1.44 bright fringes on one side of central amximum

or either sides is is 1.44*2 = 2.88 = 3 bright frines

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