Question

In figure, if a parallel beam of white light is incident on the plane of the slit, then the distance of the nearest white spot on the screen form O is [assume d < < D , λ < < D ]

• A. $\frac{\lambda_r D}{d}$
• B. $\frac{\lambda_v D}{d}$
• C. $\frac{2 \lambda_v D}{d}$
• D. $\frac{\lambda_r D}{2d}$

Answer 1

Answer: (A), (C)

$\frac{\lambda_r D}{d}$

Answer 2

In single-slit diffraction of white light, the central maximum is white. The first colored fringes appear adjacent to the central maximum. The first white fringe after the central maximum is formed when the first minimum of red light coincides with the second minimum of violet light. This condition is $d \sin \theta = 1 \cdot \lambda_r = 2 \cdot \lambda_v$. The position on the screen is given by $y = D \tan \theta$. For small angles, $y \approx D \sin \theta$. Using the condition $d \sin \theta = \lambda_r$, we get $\sin \theta = \frac{\lambda_r}{d}$. Therefore, the position of the first white fringe is $y = D \frac{\lambda_r}{d}$.