1) Light of wavelength 420nm goes through a single narrow slit of width a. The a

Question

1) Light of wavelength 420nm goes through a single narrow slit of width a. The angle between the first minimum on the left and the first minimum on the right is 2 degrees. What is d (in nm)?

2) A double slit diffraction pattern has an intensity envelop around the central maximum. And inside it there are n fringes. If the wavelength is 420nm and d=0.200 nm and a = 45 micrometers, then what is n?

3) A double slit diffraction pattern has an intensity envelope around the central maximum. And inside it there are n fringes. If the wavelength is 420nm and d=0.200 nm and a = 45 micrometers, then what is the ratio of the intensity of the central fringe compared to the third fringe? (This should be bigger than one.)

4) Young’s Experiment is performed with wavelength 420nm and the slits are 2mm apart. How far away should you place a screen so that the closest fringes are 2mm apart?

5) You wish to coat some glass (n=1.6) with a thin film of transparent material (n=1.33) so that light of wavelength 420nm (in vacuum) does not reflect. What minimum thickness (in nm) do you need?

Explanation / Answer

1) lambda=420nm

ø=2°

d*sinø=m*lambda...d=1*420nm/sin2

d = 461.9 nm

2)

We know tha,   Yn = m*lambda*D / a

Yn = (1) (420 x 10-9 m) (0.2 x 10-9 m) / (45 x 10-6 m)

Yn = 1.86 x 10-12 m

4)

The difference between two fringes is lambda*D / a

2*10^-3=420*10^-9*D/2*10^-3

D=9.523 m

5)

2nt = m*lambda

t = (1) (420 x 10-9 m) / 2 (1.6)

t = 131.2 nm

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