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Wave Optics

Question
CBSEENPH12039877

A beam of light of straight lambda = 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is,

  • 1.2 cm

  • 1.2 mm

  • 2.4 cm

  • 2.4 mm

Solution

D.

2.4 mm


From the above figure,

tan space theta space equals space fraction numerator begin display style bevelled x over 2 end style over denominator 2 end fraction
For small straight theta and when straight theta is counted in rad, tan almost equal tostraight theta
So, 
space space space space space space straight theta almost equal to fraction numerator begin display style bevelled straight x over 2 end style over denominator 2 end fraction
rightwards double arrow space space straight lambda over 9 space almost equal to space straight x over 4
straight x space equals space fraction numerator 4 straight lambda over denominator straight a end fraction equals fraction numerator 4 space straight x space 600 space straight x space 10 to the power of negative 9 end exponent over denominator 10 to the power of negative 3 end exponent end fraction space straight m
space space space equals space 24 space straight x space 10 to the power of negative 4 end exponent space straight m
space space space equals space 2.4 space straight x space 10 to the power of negative 3 end exponent space straight m
space space space equals space 2.4 space mm

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