Question

Ordinary white passes through a diffraction grating having 10,000 slits per centimeter, i.e. a slit separation of d = 1.00 X 10-6 m, and casts a diffraction pattern on a screen. You measure the angular separation between the central white fringe and the blue stripe in the first (m = 1) rainbow as 23.6 degrees. From this information, calculate the wavelength of blue light.

Answer 1

Answer on Question #58618, Physics / Optics

Ordinary white passes through a diffraction grating having 10,000 slits per centimeter, i.e. a slit separation of $d = 1.00 \times 10^{-6}$ m, and casts a diffraction pattern on a screen. You measure the angular separation between the central white fringe and the blue stripe in the first ( $m = 1$ ) rainbow as 23.6 degrees. From this information, calculate the wavelength of blue light.

Solution:

The condition for maximum (bright spot) is

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

where $m = 1$ is order of interference, $d = 1 \times 10^{-6} \, \text{m}$ .

Thus,

$$\lambda = \frac {d \sin \theta}{m} = \frac {1 \cdot 1 0 ^ {- 6} \cdot \sin 2 3 . 6 {}^ {\circ}}{1} = 4 \cdot 1 0 ^ {- 7} \mathrm {m} = 4 0 0 \cdot 1 0 ^ {- 9} \mathrm {m} = 4 0 0 \mathrm {n m}$$

Answer: $400 \cdot 10^{-9} \, \text{m} = 400 \, \text{nm}$

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