Light of wavelength 381 nm (in vacuum) is incident on a diffraction grating that

Question

Light of wavelength 381 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 0.20 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.) y = (b) If the entire apparatus is submerged in water (nwater = 1.33), what is the distance y? y =

Explanation / Answer

A) Y = mR/d

   Y = 2*381*10^-9*0.2/(1.2*10^-5)

   Y = 127*10^-4

Y = 0.0127 m

B)when in air, n= c/v

v = c/n = 3*10*8m/s

when it water

v = 3*10^8/1.33 = 2.25*10^8 m/s

since velocity decreased y also decreases to 0.0095 m

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