When blue light of wavelength 460 nm falls on a single slit, the first dark bands on either side of center are separated by 45.0°. determine the width of the slit. express your answer to three significant figures and include the appropriate units.

width of slit =1.23× 10⁻⁶ m  

Explanation:

we know the condition of diffraction minima,

d sin θ = n λ

λ = wavelength     θ = angle between the central maxima and 1st  minima

d = slit width

for first minima  n = 1

now,

d =

d =

d = 1228 × 10⁻⁹ m  = 1.228× 10⁻⁶ m

d =  1.23× 10⁻⁶ m

width of slit =1.23× 10⁻⁶ m  

it may be wrong but i think its a

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west