COMEDK 2024 Shift 2 Paper

The angular width of the central maximum in the single-slit diffraction pattern is given by:
sin‌θ=‌

λ

a

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=‌

λ

a

=‌

800×10−9m

0.020×10−3m

=0.04‌rad
Now, in Young's double-slit experiment, the angular position of the nth bright fringe is given by:
sin‌θn=n‌

λ

d

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

λ

d

≤‌

λ

a

‌n≤‌

d

a

=‌

0.20×10−3m

0.020×10−3m

=10
Since 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.