Q58P A grating has 600 rulings/mm and... [FREE SOLUTION]

Chapter 36: Q58P (page 1113)

A grating has 600 rulings/mm and is 5.0 mm wide. (a) What is the smallest wavelength interval it can resolve in the third order at ? (b) How many higher orders of maxima can be seen?

Short Answer

Expert verified

The smallest wavelength interval it can resolve in the third order is $0.056 n m$ .
No higher orders of the maxima can be seen.

Step by step solution

The resolving power

It is known the resolving power of a grating is given by $R = Nm = \frac{位_{a v g}}{鈭� 位}$ , where is $N$ the number of rulings in the grating and $m$ is the order of the lines $位_{avg}$ , is the average of wavelengths and $鈭� 位$ is the separation.

The wavelength interval

Here, the order is $m = 3$ . So, the wavelength interval can be obtained as follows:

$螖位 = \frac{位}{N m} = \frac{500 鈥� nm}{600 脳 5.0 脳 3} = 0.056 鈥� nm$

Thus, the smallest wavelength interval it can resolve in the third order is $0.056 鈥� nm$ .

(b)

To find the highest order of the maxima, we have $\sin 胃 = \frac{m_{m a x} 位}{d} < 1$ . So, the value of highest order of the maxima is:

$m_{\max} < \frac{d}{位} < \frac{\frac{1}{600}}{500 脳 10^{- 6} mm} < 3.3$

Since, the order can be a whole number, so, the highest order is 3.

Thus, no higher orders of the maxima can be seen.

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91影视

A grating has 600 rulings/mm and is 5.0 mm wide. (a) What is the smallest wavelength interval it can resolve in the third order at ? (b) How many higher orders of maxima can be seen?

Short Answer

Step by step solution

The resolving power

The wavelength interval

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