Physics, 15.07.2020 05:01 teamroper35

A grating having 5000 lines/cm is used with light of wavelength 633 nm. How many total maxima (count central maxima plus all those on either side of the central maxima) are produced

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Answer from: pareshrr

The total number of maxima produced is m_T = 7 maxima

Explanation:

From the question we are told that

The number of lines per cm is $n = 5000 \ lines/cm$

The wavelength of the light is $\lambda = 633 nm = 633 *10^{-9} \ m$

Now the distance between the lines is mathematically evaluated as

$d = \frac{1}{n}$

substituting values

$d = \frac{1}{5000}$

$d = \frac{1 *10^{-2}}{5000}$ N/B - this statement convert it from cm to m

$d = 2 *10^{ -6} \ m$

Generally the condition for diffraction i mathematically represented as

$dsin(\theta ) = m \lambda$

at maximum $\theta = 90 ^o$

$d sin (90) = \lambda m$

here m is the number of maxima

Thus making m the subject we have

$m = \frac{d sin (90)}{ \lambda }$

So $m = \frac{2*10^{-6} sin (90)}{ 633 *10^{-9}}$

m = 3.2

=> m =3

Now the total number of maxima would include the bright fringe(3) and dark fringe (3) plus the central maxima (1)

Thus

m_T = 3 + 3 +1

m_T = 7 maxima

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A grating having 5000 lines/cm is used with light of wavelength 633 nm. How many total maxima (count...

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