# Problem: A monochromatic beam of light of wavelength 550 nm is sent through each of the following six optical slides.Rank these scenarios on the basis of the angle of the first interference maximum.Rank from largest to smallest. To rank items as equivalent, overlap them.a.) difraction grating with 1000 lines/cmb.) single slit slide with width .04mmc.) single slit slide with width .01mmd.) double slit slide with spacing .08mme.) diffraction grating with 500 lines/cmf.) double slit slide with spacing .02mm

###### FREE Expert Solution

a)

Slit width, d = 1/1000 cm = 1 × 10-3 cm = 1 × 10-5 m

For bright fringe, dsinθ = mλ

m = 1 for the first bright fringe. Therefore:

$\begin{array}{rcl}\mathbf{\theta }& \mathbf{=}& \mathbf{s}\mathbf{i}{\mathbf{n}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\frac{\mathbf{m}\mathbf{\lambda }}{\mathbf{d}}\mathbf{\right)}\\ & \mathbf{=}& \mathbf{s}\mathbf{i}{\mathbf{n}}^{\mathbf{-}\mathbf{1}}\mathbf{\left[}\frac{\mathbf{\left(}\mathbf{1}\mathbf{\right)}\mathbf{\left(}\mathbf{550}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{\right)}}{\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{5}}}\mathbf{\right]}\end{array}$

θ = 3.2°

###### Problem Details

A monochromatic beam of light of wavelength 550 nm is sent through each of the following six optical slides.

Rank these scenarios on the basis of the angle of the first interference maximum.

Rank from largest to smallest. To rank items as equivalent, overlap them.

a.) difraction grating with 1000 lines/cm

b.) single slit slide with width .04mm

c.) single slit slide with width .01mm

d.) double slit slide with spacing .08mm

e.) diffraction grating with 500 lines/cm

f.) double slit slide with spacing .02mm