Light of wavelength 412 nm (in vacuum) is incident on a diffraction grating that

Question

Light of wavelength 412 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 0.16 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)

y = m * lambda * D / d

y = (2 * 412 * 10^-9 * 0.16) / ( 1.2 * 10^-5)

y = 0.010986 m

b)

Now lambda = 412/1.33 = 309.77 nm

y = m*lambda*D/d

y = (2 * 309.77 * 10^-9 * 0.16) / (1.2 * 10^-5)

y = 0.00826053 m

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