Question

A diffraction grating has 5560 lines/cm . When a beam of monochromatic light goes through it, the second pair of bright spots occurs at ±26.0 cm from the central spot on a screen 42.6 cm past the grating.

A) What is the wavelength of this light? in nm

B) How far from the central spot does the next pair of bright spots occur on the screen?

Answer 1

Solution)

A)

d= 1/(5560 per cm*100cm/m) = 1.798*10-6 m

Also,

tanθ = 26/42.6

θ = 31.39 degrees

We know,

dsinθ = mλ

where m = 2

So,

1.798*10-6 m * sin(31.39) = 2 * λ

λ = 4.68*10-7 m = 470 nm

=============

B)

We know,

dsinθ = mλ where m = 3

1.798*10-6 * sinθ = 3 * 4.70*10-7

sin θ = 3 * 4.70*10-7 / 1.79*10-6

sinθ = 0.78771

θ = 51.97 degrees

Also,

tan 51.97 = distance/42.6

distance = 42.6 * tan 51.97 = 54.46 cm

===========