Q29E - University Physics with Modern Physics

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.

Step-by-Step Solution

Answer

      1. The wavelength of the light is  

      2. The second-order deviation of the wavelength is

Step 1: 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

Step 2: 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