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NUMERICAL 1 [2082]

A parallel beam of monochromatic light is incident on diffraction grating having 500 lines/mm to get second order maxima at [latex]30^o[/latex]. Calculate the wavelength of light used. [3]
Ans: [latex]5\times 10^{-7}[/latex] m

Solution

Given,

No. of lines per unit length (N) = 500 lines / mm = 500 x 103 lines/m

Wavelength [latex](\lambda)[/latex] =?

Order of diffraction (n) = 2

Angle [latex](\theta)[/latex] = 30o

We know that,

[latex]d = \frac{1}{N}[/latex]

Or,  [latex]d = \frac{1}{500\times 10^3} = 2\times 10^{-6}m[/latex]

Now, dSin [latex]\theta = n\lambda[/latex]

Or, dSin[latex]30^o = 2\lambda[/latex]

Or, [latex]\lambda = \frac{d sin30^o}{2}[/latex]

Or, [latex]\lambda = \frac{(2\times 10^{-6})\times 0.5}{2}[/latex]

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