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Anika [276]
2 years ago
12

A grating has 2000 slits/cm/cm. How many full spectral orders can be seen (400 to 700 nmnm) when it is illuminated by white ligh

t
Physics
1 answer:
Anton [14]2 years ago
6 0

With the use of the formula SinФ = nλ / d, there are 16 spectral orders which can be seen when it is illuminated by white light.

Given that a grating has 2000 slits/cm. That is,

d = 0.01 / 2000

d = 5 x 10^{-6} m

The wavelength λ = (700 - 400) nm

λ = 300 x 10^{-9} m

To calculate how many full spectral orders that can be seen (400 to 700 nm) when it is illuminated by white light, we will use the below formula

SinФ = nλ / d

Φ = Sin^{-1} (nλ / d)

When n = 1

Φ = Sin^{-1}(300 x 10^{-9}/ 5 x 10^{-6} )

Φ = 3.4 degrees

when n = 2

Φ = Sin^{-1}(2 x 300 x 10^{-9}/ 5 x 10^{-6} )

Ф = 6.9 degrees

When n = 3

Ф = Sin^{-1}(3 x 300 x 10^{-9}/ 5 x 10^{-6} )

When n = 16

Ф = Sin^{-1}(16 x 300 x 10^{-9}/ 5 x 10^{-6} )

Ф = Sin^{-1}(0.96)

Ф = 73.7 degrees

when n = 17

Ф = Sin^{-1}(17 x 300 x 10^{-9}/ 5 x 10^{-6} )

Ф = Sin^{-1}(1.05)

Ф = Error ( that is, it does not exist)

Therefore, there are 16 spectral orders which can be seen when it is illuminated by white light.

Learn more about double slit here: brainly.com/question/4449144

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