COMEDK 2024 Shift 1 Paper

In a single slit diffraction experiment, the width of the central maxima is given by the diffraction pattern formula derived from the Huygens-Fresnel principle. The position of the first minima in the diffraction pattern is given by:
asin‌(θ)=nλ
where a is the slit width, θ is the angle of the diffraction minimum, n is the order of the minimum (for the first minimum, n=1 ), and λ is the wavelength of the light used.
The angular width of the central maxima is approximately twice the angle to the first minimum:
∆θ=‌

2λ

a

When projecting this onto a screen at a distance D, the width of the central maximum car be approximated by:
β=2D‌tan(θ)≈2D(‌

λ

a

)
If the slit width a is doubled, say to 2a, then the new width of the central maximum β′ becomes:
β′=2D(‌

λ

2a

)=‌

β

2

Thus, if the slit width is doubled, the corresponding width of the central maxima will be: Option C: ‌

β

2

.