White light containing wavelengths from 400 nm to 750 nm strikes a grating conta

Question

White light containing wavelengths from 400 nm to 750 nm strikes a grating containing 6,500 lines/cm. When viewed on a screen 1.5 m away, what is the distance along the screen between the second order maxima for the light at the red end of the spectrum and the third order of maxima for light at the violet end of the spectrum that are located on the same side of the central maximum? Provide a rough sketch of the situation.

Please show all work so I can follow along easily. If possible proved a sketch of situation.

Explanation / Answer

The formula that applies is y/L = m(wavelength)/d

d is the inverse of lines per cm, converted to meters. That is 1/650000

For the violet

y/1.5 = (3)(400 X 10-9)(650000)

y = 1.17 m

For red

y/1.5 = (2)(750 X 10-9)(650000)

y = 1.4625 m

The difference is 1.4625 - 1.17= .2925 m

That is 29.3 cm

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