Question

When a light with wavelength ? = 400nm passes through a single slit, it creates a central peak that is 4.8 cm wide on a screen that is 2.3m from the single slit. i) Determine the width of the slit.

Answer 1

18.7

Step-by-step explanation:

We can use the equation for single-slit diffraction to solve for the width of the slit:

sin(θ) = λ / (w)

where θ is the angle between the central peak and the first minimum, λ is the wavelength, and w is the width of the slit.

We can rearrange this equation to solve for w:

w = λ / sin(θ)

To find θ, we can use the small angle approximation:

θ = tan(θ) = (y) / (L)

where y is the width of the central peak on the screen and L is the distance from the slit to the screen.

Plugging in the given values, we get:

θ = tan(θ) = (4.8 cm) / (2.3 m) = 0.021

Using the wavelength given in the problem, we get:

w = (400 nm) / sin(0.021) = 18.7 µm

Therefore, the width of the slit is approximately 18.7 µm.