A beam of bright red light of wavelength 654 nm passes through a diffraction grating. Enclosing the space beyond the grating is a large semi cylindrical screen centered on the grating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on the screen. Find (a) the maximum and (b) the minimum possible values for the slit separation in the diffraction grating.

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Malcolm Mcbride · Accepted Answer

(a) The maximum value of slit separation:Since there are 15 bright spots which include central maxima and 7-7 spots on each side of maxima. therefore there is a maximum of 7 spots.The equation for the diffraction grating is given by,  d  sin  ⁡  θ  =  n  λSlit width will be maximum when,   sin  ⁡  θ  =  1 and n=7  ∴      d          max        =            d      λ              sin      ⁡      θ          =            7      ×      654       nm        1      =  4578   nmAnswer:   ∴      d          max        =  4578   nm

badlife18va · Accepted Answer

(b) The minimum value of slit separation:The equation for the diffraction grating is given by,  d  sin  ⁡  θ  =  n  λSlit width will be minimum when,   n  =  0  ∴      d          m      i      n        =            n      λ              sin      ⁡      θ          =            0      ×      654       nm              sin      ⁡      θ          =  0   nmAnswer:   ∴      d          m      i      n        =  0   nm

A beam of bright red light of wavelength 654 nm passes through a diffraction grating.

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