A 1.6-cm-wide diffraction grating has 1000 slits. It is illuminated by light of wavelength 530 nm. What are the angles of the first two diffraction orders?

By using the Huygens formula, the angles of the first two orders are 4 degrees and 8 degrees approximately.

Given that a 1.6cm wide diffraction grating has 1000 slits.

The slit spacing = (1.6 x ) / 1000

The slit spacing = 1.6 x

Also, it is given that It is illuminated by light of wavelength 530 nm

Sin∅ = nλ/d

When n = 1

Sin∅ = 530 x /1.6 x

Sin∅ = 0.033125

∅ = ( 0.033125)

∅ = 1.898 x 2

The angle of the first order = 2∅

2∅ = 4 degrees approximately

When n = 2

Sin∅ = nλ/d

Sin∅ = 2 x 530 x /1.6 x

Sin∅ = 0.06625

∅ = ( 0.06625)

The angle of the second order = 2∅

2∅ = 3.7986 x 2

2∅ = 8 degrees approximately

Therefore, the angles of the first two orders are 4 degrees and 8 degrees approximately.

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Explanation:

We can find the distance between any two adjacent slits by using

We know that the angle of the mth fringe is given by                  

Using the same way:  

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