Find the angle of the blue ( ? = 420 n m ) component of the first-order maxima i

Question

Find the angle of the blue (? = 420 nm) component of the first-order maxima in a pattern produced by a diffraction grating with 9500lines/cm?(theta 1A___)

Find the angle of the blue (? = 420 nm) component of the second-order maxima in a pattern produced by a diffraction grating with 9500lines/cm? (theta 1b__)                         

Find the angle of the red (? = 680 nm) component of the first-order maxima in a pattern produced by a diffraction grating with 9500lines/cm .(theta 1a__)

Find the angle of the red (? = 680 nm) component of the second-order maxima in a pattern produced by a diffraction grating with 9500lines/cm . (theta 1b__)

Please show work thank you

Explanation / Answer

Part A)

Blue first order

Apply sin(angle) = m(wavelength)/d

d is the inverse of the lines per cm, converted to meters, that is 1/950000 = 1.053 X 10^-6 m

sin(angle) = (1)(420 X 10^-9)/(1.053 X 10^-6)

angle = 23.5 degrees

Part B

Blue second order

sin(angle) = (2)(420 X 10^-9)/(1.053 X 10^-6)

angle = 52.9 degrees

Part C)
Red first order

sin(angle) = (1)(680 X 10^-9)/(1.053 X 10^-6)

angle = 40.2 degrees

Part D)

Red second order

sin(angle) = (2)(680 X 10^-9)/(1.053 X 10^-6)

Impossible - Will not be seen. The angle is greater than 90 degrees since the sin is greater than 1.

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