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

width of slit =1.23× 10⁻⁶ m

Step-by-step 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 =
`(n \lambda)/(sin \theta)`

`\theta = (45^0)/(2) = 22.5^0`

d =
`(1* 460 * 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