Incident light of wavelength λ=800‌nm produces a diffraction pattern on a screen 1.5 m away when it passes through a single slit of width 0.5 mm . The distance between the first dark fringes on either side of the central bright fringe is
To find the distance between the first dark fringes on either side of the central bright fringe in a single-slit diffraction pattern, we need to use the formula for the position of the dark fringes. The position of the first dark fringe is given by: y=‌
mλL
a
where: m is the order of the dark fringe ( m=1 for the first dark fringe) λ is the wavelength of the light L is the distance from the slit to the screen a is the width of the slit Given:
‌λ=800‌nm=800×10−9m ‌L=1.5m ‌a=0.5‌mm=0.5×10−3m For the first dark fringe (m=1) : y1=‌
1×800×10−9m×1.5m
0.5×10−3m
Simplifying: ‌y1=‌
800×1.5×10−9+3
0.5
m ‌y1=‌
1200×10−6
0.5
m ‌y1=‌
1200×10−6
0.5
m ‌y1=2400×10−6m ‌y1=2.4‌mm This is the distance from the central bright fringe to the first dark fringe on one side. Therefore, the total distance between the first dark fringes on either side of the central bright fringe is: 2×2.4‌mm=4.8‌mm Thus, the correct answer is: Option D: 4.8 mm