A diffraction grating is used to resolve 474.7 nm and 474.72 nm light, at 3rd or

Question

A diffraction grating is used to resolve 474.7 nm and 474.72 nm light, at 3rd order. The minimum number of lines in the grating is 7912.

If the 4th order maximum is visible for this grading for 474.7 nm and 474.72 nm light, what is the smallest line spacing possible (in m)? I know this is 1.8988. I need help with these:

a. What is the grating specification (in lines/cm)?

b. What is the minimum width of the grating (in cm)?

c. If the pattern is projected on a screen located 106.5 cm away, how far from the central maximum is the 3rd maximum for 474.7 nm light located (in cm)?

Please help!!

Explanation / Answer

a.grating specification = 1/1.8988× 10^-6 = 5366.5 lines/cm

b. minimum width of grating = 7912 × 1.8988 × 10^-6 = 1.5cm

c. d Sin theta = m lemda

dy/D = m lemda thus y = m lemda D / d = 3 × 474.7 ×10^-9× 106.5/1.8988×10^-6 = 79.8 75cm

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