A grating with 1500 lines/cm has blue light with a wavelength of 490 nm incident on it. a. You measure a diffraction angle of 12.7 ∘ to one of the maxima. Which order bright spot is this? b. How far from the grating should you place a screen in order for the second order minima (dark spot) to occur 6.8 cm from the central maxima?

Question

A grating with 1500 lines/cm has blue light with a wavelength of 490 nm incident on it. a. You measure a diffraction angle of       12.7    ∘   to one of the maxima. Which order bright spot is this? b. How far from the grating should you place a screen in order for the second order minima (dark spot) to occur 6.8 cm from the central maxima?

na1p1a2pafr · Accepted Answer

The equation for diffraction of light is  d  sin  ⁡  θ  =  m  λwhere d is the slit widthm is the order of diffraction  tan  ⁡  θ  =      distance of second minima from central maxima    distance of screen from grating    =      y    D  The angle of diffraction is 12.7 degree, wavelength is 490 nm. There are 1500 lines / cm. The slit width is   d  =      1    1500       c  m  =  6.66  ×      10          −      4           c  m  =  6.66  ×      10          −      6        mtherefore from equation  m  =            6.66      ×              10                  −          6                    sin      ⁡              12.7        ∘                    490      ×              10                  −          9                    diffraction angle for order 2 minima is  sin  ⁡  θ  =            2      ×      490      ×              10                  −          9                            6.66      ×              10                  −          6                        θ  =  8.45   degreesNow from equation , distance of screen is  D  =      y          tan      ⁡      8.45        =      6.8    0.418       c  mAnswer:a) Order is 3b) distance of screen from grating is 45.9 cm

How far from the grating a screen for the second order minima to occur 6.8cm from the central maxima

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