Question

4. Light, with 550 nm wavelength, is used to illuminate double slits which are separated of -5 3.5 x 10 m. A screen is placed 1.25 m from the slits. a. Find the angle of the first bright fringe. (5 points) b. Find the angle of the third bright fringe. (5 points) A diffraction grating has 3 x 106 lines per meter. The grating is illuminated by monochromatic plane waves of wavelength 600 nm at normal incidence that forms an interference pattern on a screen located 0.50 m away c) Find the angle the first bright fringe. (5 points) d) Find the angle corresponding to the second bright fringe. (5 points) e) Find the angle of the third bright fringe. (5 points) f) Find the frequency of an electromagnetic wave that has a wavelength 600 nm. (5 points)

Answer 1

$\lambda=550nm$

Double slit separation, d= 3.5*10^-5m

Screen distance, D= 1.25m

For double slit, the bright condition is given by,

$d\sin\theta =m \lambda$

So, $\theta =\sin^{-1}(\frac{m \lambda}{d})$

a) For m=1,

$\theta_1 =\sin^{-1}(\frac{1* \lambda}{d})=\sin^{-1}(\frac{1* 550*10^{-9}}{3.5*10^{-5}})=0.9004^o$b) For m=3,

$\theta_3 =\sin^{-1}(\frac{3* \lambda}{d})=\sin^{-1}(\frac{3* 550*10^{-9}}{3.5*10^{-5}})=2.702^o$