Question

You are being asked to determine if there is any oxygen present in an unknown mixture of gas. You know that when oxygen is made to glow by placing a large potential difference across it, it will produce light most brightly at the following wavelengths (in nanometers): 408, 419, 441, and 465. You use a strong power supply to make a sample of this gas mixture glow then use a spectroscope to split the light into its components. The spectroscope contains an interference grating with 500 ± 10 ?????⁄??.

a. Assuming the mixture does contain oxygen, draw a labeled diagram showing what the interference pattern produced by that oxygen would look like.

b. Choose three features of the pattern. Determine the angle (with respect to the center of the pattern) that each of these features would appear at. For example, you could choose to find the angle for m = 0 for all wavelengths, and m = +1 for the 408 nm and 465 nm wavelengths. Or you could determine the angle at 3 different features – the choice is yours.

Answer 1

slit separation d = 1/500 mm = 2000 nm

for interference

dsin = m for m=0 all wave length will be at ) , i.e central bright spot.

m=1 ; sin = /d

(nm)	408	419	441	465
sin	0.204	0.2095	0.2205	0.2325
(deg)	11.77	12.09	12.73	13.55

m=2 ; sin = 2/d

(nm)	408	419	441	465
sin	0.408	0.419	0.441	0.465
(deg)	24.08	24.77	26.17	27.71
m=3; sin = 3/d
sin	0.612	0.6285	0.6615	0.6975
(deg)	37.73	38.94	41.41	44.23

1) for the third order m=3 all the wavelength are well separated

2) for m=2 , second order 408 and 419 are close and not well separated. 441 and 465 are some what close but can be distinguished

3) for m=1 , first order, 441 and 465 are better separated compared to the other two lines.

In general the intensity of the higher order lines is less compared to the lower order of m