• A diffraction grating has 5000 lines per cm. The angle between the central maximum and the first order maximum is 11.8e. What is the wavelength of the light? 

  •  

  • A) 183 nm B) 409 nm C) 138 nm D) 637 nm 

     

  • Light of wavelength 580 nm is incident on a slit of width 0.300 mm. An observing screen is placed 2.00 m from the slit. Find the position of the first order dark fringe from the center of the screen.

    A) 3.9 mm B) 1.9 mm C) 0.26 mm D) 7.7 mm 

  • Expert Answers

    An illustration of the letter 'A' in a speech bubbles

    The equation necessary to solve this problem is:

    m`` =dsin``

    In this problem m is equal to 1 as we have been given the angle of the first order maximum: ``

    The above equation is then simplified to: `` =dsin``

    In order to calculate the slit spacing, d, we divide 1 cm by the...

    Unlock
    This Answer Now

    Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

    Start your 48-Hour Free Trial

    The equation necessary to solve this problem is:

    m`` =dsin``

    In this problem m is equal to 1 as we have been given the angle of the first order maximum: ``

    The above equation is then simplified to: `` =dsin``

    In order to calculate the slit spacing, d, we divide 1 cm by the diffraction gradient: d = 1/5000 = 0.0002 cm.

    In order to simplify the conversion of the wavelength units to nanometers (nm), this spacing is converted to a unit of meters: d = 0.0002/100 = 2.0x10^-6 m

    Substituting the known parameters into the equation for ``  we get:

    = (2.0x10^-6)sin(11.8) = 4.09x10^-7 m = 409 nm

    Therefore, the correct answer to this question is B) 409 nm.

    If you still require a response to your second question, please post it as a new question.

    Approved by eNotes Editorial Team