Question

A double slit with a spacing of 0.054 mm between the slits is 1.57 m from a screen.

1.) If yellow light of wavelength 567 nm strikes the double slit, what is the separation between the zeroth- and first-order maxima on the screen? (Answer in meters)

2.) If blue light of wavelength 426 nm strikes the double slit, what is the separation between the second- and fourth-order maxima? (Answer in meters)

Answer 1

1)

The maxima condition for interference is

d sin ( theta ) = m ( lamda )

Y = L tan ( thate )

Fro small angles

m ( Lamda ) / d = Y / L

Y = m ( Lama ) L / d

= ( 1) ( 567 *10^ -9 m ) (1.57 m ) / ( 0.054 *10^ -3 m )

= 0.016 m

2)

Y1 = m ( Lama ) L / d

= ( 4) ( 426 *10^ -9 m ) (1.57 m ) / ( 0.054 *10^ -3 m )

= 0.0495 m

Y2 = m ( Lama ) L / d

= ( 2) ( 426 *10^ -9 m ) (1.57 m ) / ( 0.054 *10^ -3 m )

= 0.0247 m

Y1 - Y2 = 0.0495 m - 0.0247 m = 0.0247 m