Hello, i need some help with questions #5 & #6. PLEASE SHOW STEPS! i cannot figu

Question

Hello,

i need some help with questions #5 & #6. PLEASE SHOW STEPS! i cannot figure these out and really appreciate your help! Equation #39.1 for question #6 is n-lamba= dsin theta. with d = (1/6000). thanks again!

Why are the higher-order spectra more accurate than the first-order spectrum in determining wave-lengths of light? Angle measurements get smaller percentage errors and the angle gets larger 1 st order : 10 1 = 10 % error 2nd order: 20 1 = 5 % error The absolute value of the uncertainty is constant, so the percentage error gets less as angle increases. A grating having 15.000 lines per inch is used lo produce a spectrum of the light from a mercury are shining through a slit. What is the angle between the first-order green line and the second-order green line See Experiment 37 for the wavelength of the mercury green line. Consider two rays coming from adjacent slits In a grating of grating constant d and intersecting at the point where they strike a distant screen. Use the rule for constructive interference (sec Experiment 38) to derive Equation 39.1. the two rays are almost parallel.

Explanation / Answer

5. first order will be given by
lambda = d sin theta

d = 1/15000 in = 1.69E-6 m

theta = arcsin(546.0E-9/1.69E-6)= 18.85 degrees

second order

2 lamdba = d sin theta

so theta =arcsin(2*546.0E-9/1.69E-6) = 40.25

so angle between = 40.25-18.85= 21.4 degrees

6) so if they are almost parallel, one ray will go a bit further distance than the other

that distance = d sin theta

to be constructive this has to be an integer number of wavelengths
so m lambda = d sin theta

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