Question

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.

Answer 1

Answer:

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 =$\dfrac{n \lambda}{sin \theta}$

$\theta = \dfrac{45^0}{2} = 22.5^0$

d =$\dfrac{1\times 460 \times 10^{-9}}{sin 22.5^0}$

d = 1228 × 10⁻⁹ m  = 1.228× 10⁻⁶ m

d =  1.23× 10⁻⁶ m

width of slit =1.23× 10⁻⁶ m