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A grating is 3.4 cm wide. A spectral line of wavelength 578 nm is observed at...

A grating is 3.4 cm wide. A spectral line of wavelength 578 nm is observed at 39∘ in order 3.

The grating is made up of ---- lines. (How many?)

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Answer #1

We use the equation for a grating

d = distance between the lines in a grating

= angle = 39o

m = order = 3

= wavelength = 578 nm = 578 x 10-9 m

So, d = (3 x 578 x 10-9 )/sin(39) m = 2.76 x 10-6 m = 2.76 x10-4 cm

No. of lines per cm = 1/d = 1/2.76 x10-4 cm-1 = 3623.19 cm-1

Width of the grating = 3.4 cm

No of lines = 3623.19 x 3.4 lines = 12318.846 lines = 12319 lines (rounding off)

Hence, there are 12319 lines in the grating

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