Light of wavelength 414 nm (in vacuum) is incident on a diffraction grating that

Question

Light of wavelength 414 nm (in vacuum) is incident on a diffraction grating that has a slit separation of 1.2 × 10-5 m. The distance between the grating and the viewing screen is 0.17 m. A diffraction pattern is produced on the screen that consists of a central bright fringe and higher-order bright fringes (see the drawing). (a) Determine the distance y from the central bright fringe to the second-order bright fringe. (Hint: The diffraction angles are small enough that the approximation tan(?) ~ sin(?) can be used.)(b) If the entire apparatus is submerged in water (nwater = 1.33), what is the distance y?

Explanation / Answer

a) d sin theta = m * lambda

d ( y / L ) = m * lambda

y = m* lambda * L / d

= (2 * 414 * 10-9 * 0.17) / (1.2 * 10-5)

y = 0.0117 m

b) lambda ' = lambda / n = 414 nm / 1.33 = 311.3 nm

y = m * lambda * L / d

= (2 * 311.3 * 10-9 * 0.17) / (1.2 * 10-5)

= 8.8 mm = 0.0088 m

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