Light of wavelength 400 nm (in vacuum) is incident on a diffraction grating that

Question

Light of wavelength 400 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

given

lamda = 400 nm

d = 1.2*10^-5 m

R = 0.17 m

a) the distance y from the central bright fringe to the second-order bright fringe, y2 = 2*lamda*R/d

= 2*400*10^-9*0.17/(1.2*10^-5)

= 0.0113 m or 1.13 cm

b) y = 0.0113/n

= 0.0113/1.33

= 8.50*10^-3 m or 8.50 mm

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