In a single-slit Fraunhofer diffraction experiment, the first secondary minimum is observed at an angle of 30^ for light of wavelength . If the same slit is now illuminated by light of the same wavelength, the angular position ( ) of the first secondary maximum is ( 30^ = 1 2 ).

Step-by-step solution

For a single-slit Fraunhofer diffraction, the condition for the n -th secondary minimum is given by: a = n For the first secondary minimum ( n=1 ) at = 30^ : a 30^ = a ( 1 2 ) = a = 2 The condition for the n -th secondary maximum is given by: a ' = (n + 1 2 ) For the first secondary maximum ( n=1 ): a ' = 3 2 Substituting a = 2 into the equation: (2 ) ' = 3 2 ' = 3 4 ' = ⁻¹ ( 3 4 ) Answer: ⁻¹(3/4)