Question

Light of wavelength 620 nm falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 15.0 degrees from the central maximum. Find the separation between the slits.

Answer 1

Answer on Question 52231, Physics, Optics

Question:

Light of wavelength $620 \, \text{nm}$ falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 15 degrees from the central maximum. Find the separation between the slits.

Solution:

Let's write the diffraction grating equation:

$$d \sin \theta = m \lambda ,$$

where, $d\sin \theta = r_2 - r_1$ is the path difference of rays, that come from the slits.

If this path difference is exactly one wavelength $\lambda$ or an integer number of wavelengths, then the two waves arrive at the screen in phase and there is a constructive interference, resulting in a bright area on the screen. For the first bright fringe, $m = 1$ , and we obtain:

$$d = \frac {\lambda}{\sin \theta} = \frac {6 2 0 \cdot 1 0 ^ {- 9} m}{\sin 1 5 {}^ {\circ}} = 2. 4 \cdot 1 0 ^ {- 6} m = 2. 4 \mu m.$$

Answer:

$$d = 2. 4 \mu m.$$

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