Question

A beam of 490 nm light is incident on a diffraction grating that has 1200 slits/mm. On a screen 9cm away,
1) Determine where the zeroth, first, and second order rays land on the screen. Do not approximate sin ⁡ ( θ ) = tan ⁡ ( θ ).
2) Re-compute assuming the entire apparatus is immersed in water, (n=1.33).

Answer 1

d=490um No. of slits per No. Of slits per m mh=1200 = 1200000 Slit widthld) - 1200000 = 8.333x10-7 (chistance of screen) D =9 cm O) 12 1 using path difference and -d Suice 1+ 490 x10 9 = 8.333x10-7 find, Sin O,= = 0.588 36.015° Tono, = y. = 9cm Tam (36.015) 16.542 cm (First hil zeroth order orde) Yo = 5 cm Second order 4,90 2x10-9 8.33x10 -7 sina, Sirio,= 1.176 (Not bossible) i It does not afflor screen.

dw = 24 490 x 10-9 T.33 -> 368.42x10-9 (il zero order Yo=oem (ii) First order It 368.42x10-9 = 8.33x10 -7 sina, - Su: O = 0.462 & 9,= 26.23 .: Tomo,= -y, = Tioma 6.33 x 9 cm - 14.46 cm c 2 + 368-42 * 10 9: 8.33667 Sm Q Sin 0,= 0.8842 62.15° Ton = Tom (62.15) - Iz qim - Y 2 = (17.03 cm