What width single slit will produce first-order diffraction minima at angles of

Question

What width single slit will produce first-order diffraction minima at angles of plusminus18degree from the central maximum with 645-nm light? mum A rectangular painting is L = 171 cm wide and L_0 = 88. 8 cm high, as indicated in the figure. At what speed, v, must the painting move parallel to its width if it is to appear to be square? (Enter your answer to 3 significant figures.) c The maximum wavelength an electromagnetic wave can have and still eject an electron from a barium surface is 501 nm. What is the work function of a barium surface? J

Explanation / Answer

sin = m/a  

While others use...

tan = m/a

here are the two solutions

Sin18 = (1)(645X 10-9)/a

a = 2.08 X 10-6 m which is 2.08 m

The other solution is

Tan18 = (1)(645 X 10-9)/a

a = 1.98 X 10-6 m which is 1.98 m

Given Data

L= 171 cm

L0 = 88.8 cm

v= c* square root [1-(L0/L)^2]

v= c* square root (1-(88.8/171)^2)

v=0.854c

The photon energy (E) must be >= work function for electrons to be ejected.
E = hf

Where h is Planck's constant and f is the frequency of the photons. In this question you are given wavelength () rather than frequency, but we also know:

c = f
Where c is the speed of light. Therefore
f = c/
E = hc/

Substituting in values:
h = 4.136 * 10^-15 eV.s , c = 2.998 * 10^8 m/s , = 501 * 10^-9 m

E = 2.48 eV

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