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Wave Optics

Question
CBSEENPH12039802

In a double slit experiment, the two slits are 1 mm apart and the screen is placed in 1 m away. A monochromatic light of wavelength 500nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of double slit within the central maxima of single slit pattern?

  • 0.2mm

  • 0.1 mm

  • 0.5 mm

  • 0.02 mm

Solution

A.

0.2mm

Given d =1 mm = 1 x 10-3 m
D =1m
straight lambda space equals space 500 nm space equals space 5 space straight x space 10 to the power of negative 7 end exponent space straight m
As space width space of space central space maxima space equals space width space of space 10 space maxima
therefore space fraction numerator 2 Dλ over denominator straight a end fraction space equals space 10 open parentheses λD over straight d close parentheses
rightwards double arrow space straight a space equals space straight d over 5 space equals space 10 to the power of negative 3 end exponent over 5 space equals space 0.2 space straight x space 10 to the power of negative 3 end exponent straight m
straight a space equals space 0.2 space mm