Concept explainers
A diffraction grating has 4 200 rulings/cm. On a 2.00 m from the grating. it is found that for a particular order m, the maxima corresponding lo two closely spaced wavelengths of sodium (589.6 nm and 589.6 nm) are separated by 1.54 mm. Determine the value of m.
The value of
Answer to Problem 38.31P
The value of
Explanation of Solution
Given info: The number a grating is
The first wavelength of sodium is
For the first order the value of
The formula to calculate separation between gratings is,
Here,
Substitute
It remains same for all the order.
The formula for diffraction grating is,
Here,
Rearrange the above expression for
Substitute
Write the expression for tan of the above angle,
Substitute
The formula for diffraction grating is for second wavelength is,
Here,
Rearrange the above expression for
Substitute
Write the expression for tan of the above angle,
Substitute
The difference between the tan of the two angle is,
Substitute
Write the formula to calculate position of central
Here,
Substitute
For the second order the value of
The formula for diffraction grating is,
Here,
Rearrange the above expression for
Substitute
Write the expression for tan of the above angle,
Substitute
The formula for diffraction grating is for second wavelength is,
Here,
Rearrange the above expression for
Substitute
Write the expression for tan of the above angle,
Substitute
The difference between the tan of the two angle is,
Substitute
Write the formula to calculate position of central
Here,
Substitute
For the third order the value of
The formula for diffraction grating is,
Here,
Rearrange the above expression for
Substitute
Write the expression for tan of the above angle,
Substitute
The formula for diffraction grating is for second wavelength is,
Here,
Rearrange the above expression for
Substitute
Write the expression for tan of the above angle,
Substitute
The difference between the tan of the two angle is,
Substitute
Write the formula to calculate position of central
Here,
Substitute
From the above calculation it is clear that only for second order the maxima of two closely spaced wavelength of sodium
Conclusion:
Therefore, the value of
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Chapter 38 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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