The angular width of the central maximum in the single-slit diffraction pattern is given by:
sin‌θ=‌where
λ is the wavelength of light, and
a is the width of the slit. Since the angle is small, we can approximate
sin‌θ≈θ.
Therefore, the angular width of the central maximum is:
θ=‌=‌| 800×10−9m |
| 0.020×10−3m |
=0.04‌radNow, in Young's double-slit experiment, the angular position of the
nth bright fringe is given by:
sin‌θn=n‌ where
d is the slit separation. Again, for small angles, we can approximate
sin‌θn≈θn.
The total angular spread of the central maximum in the single-slit diffraction pattern is
2θ. To find the number of fringes of Young's double-slit experiment that can be accommodated within this spread, we need to find the maximum value of
n such that
θn≤θ.
Therefore, we have:
‌n‌≤‌‌n≤‌=‌| 0.20×10−3m |
| 0.020×10−3m |
=10Since the central maximum itself is counted as one fringe, the total number of fringes that can be accommodated within the central maximum is
2n+1=21.
Therefore, the closest option to the answer is Option C:
20.