Question

24.73 . LIght is incident on a diffraction grating with 8600 lines/cm , and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam consists of two wavelengths, 4.5×10?7 m and 6.9×10?7 m .

Part A Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.

Answer 1

given

1 / ( a + b ) = 8600 lines/cm

or

1 / ( a + b ) = 860000 lines/m

( a + b ) sin = n

for first order bright fringes n = 1

then sin = / ( a + b )

= sin^-1 ( / ( a + b ) )

then now,

₁ = sin^-1 ( / ( a + b ) )

= sin^-1 ( 6.9 X 10^-7 X 860000)

₁ = 36.4^o

same way

₂ = sin^-1 ( / ( a + b ) )

= sin^-1 ( 4.5 X 10^-7 X 860000)

₂ = 22.77^o

now

Y_n = D tan₁

= 2.5 X tan36.4

= 1.843 m

sameway

Y_n ' = D tan₂

= 2.5 X tan22.77

= 1.05m

the linear distance between the first-order bright fringes of these two wavelengths on the screen is

Y = Y_n - Y_n '

Y = 1.843 - 1.05

Y = 0.793 m

so the linear distance between the first-order bright fringes of these

two wavelengths on the screen is Y = 0.793 m