Question

(a) What is the wavelength of light that is deviated in the first order through an angle of$\mathbf{13}\mathbf{.}\mathbf{5}\mathbf{°}$ by a transmission grating having 5000 slits / cm? (b) What is the second-order deviation of this wavelength? Assume normal incidence.

Short answer

1. The wavelength of the light is

2. The second-order deviation of the wavelength is

Step-by-step solution

Determine the wavelength of light that is deviated in the first order

The value of d can be calculated as

Now, use the formula of wavelength in relation with d

Substitute the given values

Therefore, the wavelength isof the light that is deviated in the first order through an angle

Determine the deviation of the wavelength in the second order

Use the following relation to find the deviation

Substitute the given and found values

Therefore, the second-order deviation of the wavelength is