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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Wave Optics

JIPMER 2017 · Physics · Wave Optics

White light is used to illuminate two slits in Young's double slit...

White light is used to illuminate two slits in Young's double slit experiment. The separation between the slits is bb and the screen is at a distance d(>>b)d( \gt \gt b) from the slits. At a point on the screen directly in front of one of the slits, which wavelengths are missing?White light is used to illuminate two slits in Young's double slit experiment. The separation between the slits is b

Options

  1. Abd,b3d,b5d\frac{b}{d}, \frac{b}{3 d}, \frac{b}{5 d}
  2. Bb22d,b24d,b26d\frac{b^2}{2 d}, \frac{b^2}{4 d}, \frac{b^2}{6 d}
  3. Cb2d,b23d,b25d\frac{b^2}{d}, \frac{b^2}{3 d}, \frac{b^2}{5 d}
  4. Db2d,b4d,b6d\frac{b}{2 d}, \frac{b}{4 d}, \frac{b}{6 d}

Correct answer

C. b2d,b23d,b25d\frac{b^2}{d}, \frac{b^2}{3 d}, \frac{b^2}{5 d}

Step-by-step solution

The situation is shown in the figure White light is used to illuminate two slits in Young's double slit experiment. The separation between the slits is b The path difference between the waves reaching the point PP is Δp=BP−AP=(d2+b2)1/2−d=d(1+b2d2)1/2−d≈d[1+12b2d2]−d=b22d\begin{aligned} \Delta p & =B P-A P \\ & =\left(d^2+b^2\right)^{1 / 2}-d=d\left(1+\frac{b^2}{d^2}\right)^{1 / 2}-d \\ & \approx d\left[1+\frac{1}{2} \frac{b^2}{d^2}\right]-d=\frac{b^2}{2 d} \end{aligned} For a dark band Δp=b22d=(2n−1)λ2\Delta p=\frac{b^2}{2 d}=(2 n-1) \frac{\lambda}{2} where, n=1,2,3 or λ=1(2n−1)⋅b2d\lambda=\frac{1}{(2 n-1)} \cdot \frac{b^2}{d} Hence, the missing wavelengths are b2d,b23d\frac{b^2}{d}, \frac{b^2}{3 d},b25d,....\frac{b^2}{5 d},....
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