The maximum number of dark fringes on the semi-circular screen is D. 8. Therefore , D. 8 is correct .
The angular position of each dark fringe is given by theta = sin-1(lambda/a).
If a = 4.3I, then theta = sin-1(1/4.3) = 13.45 degrees.
Since 90/13.45 = 6.69, there will be six dark fringes on either side of the semi-circle, for a total of 8 dark fringes.
The image shows a semi-circular screen surrounding a single slit. The arrows represent the light waves from the slit.
The dark fringes occur where the light waves destructively interfere.
The first dark fringe occurs at an angle of 13.45 degrees from the center of the screen.
The second dark fringe occurs at an angle of 26.9 degrees, and so on.
The sixth dark fringe occurs at an angle of 78.75 degrees.
The seventh and eighth dark fringes occur at angles greater than 90 degrees, so they are not visible on the screen.
Therefore, the maximum number of dark fringes on the semi-circular screen is 8.
Question
A single slit of width a is illuminated by light of wavelength l. If a = 4.3I, the maximum number of dark fringes on a semi-circular screen surrounding the slit is:
A. 2
B. 4
C. 6
D. 8